Computational Methods for Differential Equations

A

ADI method Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
A generalized three-dimensional KP-BBM equation On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation [Volume 13, Issue 2, 2025, Pages 682-708]
Alternating direction implicit approach Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]
Ambartsumian equation Existence and uniqueness theorems for fractional differential equations with proportional delay [Volume 13, Issue 3, 2025, Pages 904-918]
Analytical solutions On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation [Volume 13, Issue 3, 2025, Pages 1022-1036]
Ananthaswamy-Sivasankari method (ASM) A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model [Volume 13, Issue 2, 2025, Pages 432-449]
Approximate function High-order numerical solution for a class of nonlinear Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 1059-1073]
Artificial Neural Networks Solving initial value problems using multilayer perceptron artificial neural networks [Volume 13, Issue 1, 2025, Pages 13-24]
Astrophysics equations Numerical study of astrophysics equations using Bessel collocation methods of first Kind [Volume 13, Issue 2, 2025, Pages 466-478]
Attractors Analysis of a chaotic and a non-chaotic 3D dynamical system: the Quasi-Geostrophic omega equation and the Lorenz-96 model [Volume 13, Issue 3, 2025, Pages 721-741]

B

Back-propagation algorithm Solving initial value problems using multilayer perceptron artificial neural networks [Volume 13, Issue 1, 2025, Pages 13-24]
Backward bifurcation $SEI_aI_sQRS$ epidemic model for COVID-19 by using compartmental analysis and numerical simulation [Volume 13, Issue 2, 2025, Pages 592-607]
Bagley–Torvik equation On the numerical solution of the Bagley-Torvik equation using the M"{u}ntz-Legendre wavelet collocation method [Volume 13, Issue 3, 2025, Pages 968-979]
Bang-bang optimal control problems Enhancing the Legendre-Gauss-Radau pseudospectral method with sigmoid-based control parameterization for solving bang-bang optimal control problems [Volume 13, Issue 3, 2025, Pages 802-814]
Basic reproduction number $SEI_aI_sQRS$ epidemic model for COVID-19 by using compartmental analysis and numerical simulation [Volume 13, Issue 2, 2025, Pages 592-607]
Binary model Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Biorthogonal wavelet On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 885-903]
Block tridiagonal system Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
Boundary value problem A unified Explicit form for difference formulas for fractional and classical derivatives and applications [Volume 13, Issue 1, 2025, Pages 307-326]
B-splines collocation method Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem [Volume 13, Issue 2, 2025, Pages 578-591]
Burgers-Fisher’s equation Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem [Volume 13, Issue 2, 2025, Pages 578-591]

C

Caputo derivative A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation [Volume 13, Issue 1, 2025, Pages 41-60]
Caputo derivative Existence and uniqueness theorems for fractional differential equations with proportional delay [Volume 13, Issue 3, 2025, Pages 904-918]
Caputo derivative A robust numerical method to find the solutions of time-fractional Klein-Gordon equation [Volume 13, Issue 2, 2025, Pages 709-720]
Caputo derivative Solving a system of fractional Volterra integro-differential equations using cubic Hermit spline functions [Volume 13, Issue 3, 2025, Pages 980-994]
Caputo-Fabrizio fractional derivative Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative [Volume 13, Issue 2, 2025, Pages 494-504]
Caputo’s fractional derivative Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method [Volume 13, Issue 3, 2025, Pages 1047-1058]
Case and death averted Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
CFL condition On an efficient method for the fractional nonlinear Newell-Whithead-Segel equations [Volume 13, Issue 1, 2025, Pages 95-106]
Chaotic System Control of fractional-order chaotic systems under perturbations [Volume 13, Issue 3, 2025, Pages 1037-1046]
Closed-form solution A finite difference approach to solve the nonlinear model of electro-osmotic flow in nano-channels [Volume 13, Issue 3, 2025, Pages 919-926]
Compact finite difference formula A unified Explicit form for difference formulas for fractional and classical derivatives and applications [Volume 13, Issue 1, 2025, Pages 307-326]
Compact finite difference scheme An efficient high-order compact finite difference scheme for Lane-Emden-type equations [Volume 13, Issue 1, 2025, Pages 107-122]
Compressibility Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Conformable derivative Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials [Volume 13, Issue 2, 2025, Pages 373-383]
Conformable schrödinger equation Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials [Volume 13, Issue 2, 2025, Pages 373-383]
Conformable semigroup Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials [Volume 13, Issue 2, 2025, Pages 373-383]
Conic nonlinear systems LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems [Volume 13, Issue 2, 2025, Pages 505-523]
Conservation laws On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation [Volume 13, Issue 2, 2025, Pages 682-708]
Conserved vector fields Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times [Volume 13, Issue 1, 2025, Pages 249-257]
Control measure Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
Convergence analysis A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Convergence analysis Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem [Volume 13, Issue 2, 2025, Pages 578-591]
Convergence analysis Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method [Volume 13, Issue 3, 2025, Pages 1047-1058]
Convergence analysis On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 885-903]
Convergence analysis High-order numerical solution for a class of nonlinear Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 1059-1073]
Coronavirus Analysis of quarantine and liberate effects on viral infection using SEIR and Caputo $ lpha $-fractional-order model [Volume 13, Issue 3, 2025, Pages 768-782]
Cost of transaction Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]
Covid-19 Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative [Volume 13, Issue 2, 2025, Pages 494-504]
Crank Nicolson Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem [Volume 13, Issue 2, 2025, Pages 578-591]
Cross-diffusion Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior [Volume 13, Issue 1, 2025, Pages 294-306]
Cubic spline Computational approaches for analyzing fractional impulsive systems in differential equations [Volume 13, Issue 2, 2025, Pages 384-394]
Cubic Spline in Tension Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition [Volume 13, Issue 2, 2025, Pages 618-633]
Cylindrically space-times Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times [Volume 13, Issue 1, 2025, Pages 249-257]

D

Delay Differential Equations Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition [Volume 13, Issue 2, 2025, Pages 618-633]
Depletion Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Dirac integrable system Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods [Volume 13, Issue 1, 2025, Pages 61-72]
Drinfeld-Sokolov system Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Dynamical systems Dynamical systems in product Lukasiewicz semirings [Volume 13, Issue 2, 2025, Pages 676-681]
Dynamical systems Analysis of a chaotic and a non-chaotic 3D dynamical system: the Quasi-Geostrophic omega equation and the Lorenz-96 model [Volume 13, Issue 3, 2025, Pages 721-741]

E

Ebola virus model A study on the fractional Ebola virus model by the semi-analytic and numerical approach [Volume 13, Issue 3, 2025, Pages 783-801]
Ecosystem Integrated pests management and food security: A mathematical analysis [Volume 13, Issue 2, 2025, Pages 524-537]
Effective reproduction number Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
Efficient factors High-order numerical solution for a class of nonlinear Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 1059-1073]
Electro-osmotic flow A finite difference approach to solve the nonlinear model of electro-osmotic flow in nano-channels [Volume 13, Issue 3, 2025, Pages 919-926]
Entropy Dynamical systems in product Lukasiewicz semirings [Volume 13, Issue 2, 2025, Pages 676-681]
Equilibrium Integrated pests management and food security: A mathematical analysis [Volume 13, Issue 2, 2025, Pages 524-537]
Error analysis Numerical solution of different population balance models using operational method based on Genocchi polynomials [Volume 13, Issue 2, 2025, Pages 659-675]
Exact solutions Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations [Volume 13, Issue 2, 2025, Pages 608-617]
Existence and nonexistence Some existence and nonexistence results for a class of Kirchhoff-double phase systems in bounded domains [Volume 13, Issue 3, 2025, Pages 839-849]
Existence and uniqueness Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative [Volume 13, Issue 2, 2025, Pages 494-504]
Existence and uniqueness of solution Solving a class of Volterra integral equations with M-derivative [Volume 13, Issue 1, 2025, Pages 282-293]
Existence-uniqueness Existence and uniqueness theorems for fractional differential equations with proportional delay [Volume 13, Issue 3, 2025, Pages 904-918]
Exp–function method Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Exp-function method(EFM) Application of a new method for nonlinear partial differential equations of fractional order arising in fluid mechanics [Volume 13, Issue 1, 2025, Pages 1-12]

F

Fear effect A nonlinear mathematical model of the delayed predator-prey system that incorporates intraspecific predator competition and fear effect in prey [Volume 13, Issue 3, 2025, Pages 927-939]
Fictitious time integration technique A robust numerical method to find the solutions of time-fractional Klein-Gordon equation [Volume 13, Issue 2, 2025, Pages 709-720]
Finite difference A finite difference approach to solve the nonlinear model of electro-osmotic flow in nano-channels [Volume 13, Issue 3, 2025, Pages 919-926]
Finite-time bounded LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems [Volume 13, Issue 2, 2025, Pages 505-523]
Fixed point On unique solutions of integral equations by progressive contractions [Volume 13, Issue 1, 2025, Pages 183-189]
Fluid turbulence Exploring high-frequency waves and soliton solutions of fluid turbulence through relaxation medium modeled by Vakhnenko-Parkes equation [Volume 13, Issue 2, 2025, Pages 646-658]
Fordy-Gibbons-Jimbo-Miwa equation On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation [Volume 13, Issue 3, 2025, Pages 1022-1036]
Forecasting Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]
Fractional derivative A unified Explicit form for difference formulas for fractional and classical derivatives and applications [Volume 13, Issue 1, 2025, Pages 307-326]
Fractional derivatives Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method [Volume 13, Issue 2, 2025, Pages 479-493]
Fractional functional integro-differential equation Existence of solutions of Caputo fractional integro-differential equations [Volume 13, Issue 2, 2025, Pages 568-577]
Fractional integro-differential equation On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 885-903]
Fractional interval differential equation Optimal control of fractional differential equations with interval uncertainty [Volume 13, Issue 2, 2025, Pages 538-553]
Fractional-order system Control of fractional-order chaotic systems under perturbations [Volume 13, Issue 3, 2025, Pages 1037-1046]
Fractional Programming On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem [Volume 13, Issue 3, 2025, Pages 1074-1084]
Fractional Schrödinger equation A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation [Volume 13, Issue 1, 2025, Pages 41-60]
Fractional sub-diffusion equation A novel hybrid approach to approximate fractional sub-diffusion equation [Volume 13, Issue 2, 2025, Pages 420-431]
Fractional Volterra integro-differential equations Solving a system of fractional Volterra integro-differential equations using cubic Hermit spline functions [Volume 13, Issue 3, 2025, Pages 980-994]
Functional response A nonlinear mathematical model of the delayed predator-prey system that incorporates intraspecific predator competition and fear effect in prey [Volume 13, Issue 3, 2025, Pages 927-939]

G

Gas-condensate system Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Gauss-Seidel method Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
Gegenbauer wavelet functions A highly accurate wavelet approach for multi-term variable-order fractional multi-dimensional differential equations [Volume 13, Issue 3, 2025, Pages 850-869]
Generalized Drinfeld-Sokolov Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Generalized ( G′/G )-expansion method On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method [Volume 13, Issue 1, 2025, Pages 258-270]
Generalized solution Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials [Volume 13, Issue 2, 2025, Pages 373-383]
Generalized Zakharov-Kuznetsov equation On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method [Volume 13, Issue 1, 2025, Pages 258-270]
General Lagrange scaling function Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations [Volume 13, Issue 2, 2025, Pages 450-465]
Genocchi numbers Numerical solution of different population balance models using operational method based on Genocchi polynomials [Volume 13, Issue 2, 2025, Pages 659-675]
Genocchi polynomials Numerical solution of different population balance models using operational method based on Genocchi polynomials [Volume 13, Issue 2, 2025, Pages 659-675]
Globally asymptotically stable $SEI_aI_sQRS$ epidemic model for COVID-19 by using compartmental analysis and numerical simulation [Volume 13, Issue 2, 2025, Pages 592-607]
Global optimization On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem [Volume 13, Issue 3, 2025, Pages 1074-1084]
Green’s function A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Group preserving technique A robust numerical method to find the solutions of time-fractional Klein-Gordon equation [Volume 13, Issue 2, 2025, Pages 709-720]

H

Haar wavelet A study on the fractional Ebola virus model by the semi-analytic and numerical approach [Volume 13, Issue 3, 2025, Pages 783-801]
Hammerstein integral equation On unique solutions of integral equations by progressive contractions [Volume 13, Issue 1, 2025, Pages 183-189]
Hermite cubic splines On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 885-903]
Higher-order method A higher-order kernel approach for linear fourth-order boundary value problems [Volume 13, Issue 3, 2025, Pages 758-767]
High-order accuracy An efficient high-order compact finite difference scheme for Lane-Emden-type equations [Volume 13, Issue 1, 2025, Pages 107-122]
Homogeneous balance method Unveiling traveling waves and solitons of dirac integrable system via homogenous balance and singular manifolds methods [Volume 13, Issue 1, 2025, Pages 61-72]
Hopf Bifurcation Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior [Volume 13, Issue 1, 2025, Pages 294-306]
Hopf Bifurcation A nonlinear mathematical model of the delayed predator-prey system that incorporates intraspecific predator competition and fear effect in prey [Volume 13, Issue 3, 2025, Pages 927-939]

I

Immunization Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
Implicit method Finite-difference method for Hygrothermoelastic boundary value problem [Volume 13, Issue 1, 2025, Pages 157-168]
Incidence Analysis of the effect of isolation on the transmission dynamics of COVID-19: a mathematical modelling approach (R1) [Volume 13, Issue 1, 2025, Pages 123-141]
Integral boundary conditions Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition [Volume 13, Issue 2, 2025, Pages 618-633]
Integral sliding mode LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems [Volume 13, Issue 2, 2025, Pages 505-523]
Interpolating IMLS approximation Interpolating MLPG method to investigate predator-prey population dynamic with complex characters [Volume 13, Issue 2, 2025, Pages 357-372]
Interval arithmetic Optimal control of fractional differential equations with interval uncertainty [Volume 13, Issue 2, 2025, Pages 538-553]
Interval fractional calculus Optimal control of fractional differential equations with interval uncertainty [Volume 13, Issue 2, 2025, Pages 538-553]
Interval iterative method Optimal control of fractional differential equations with interval uncertainty [Volume 13, Issue 2, 2025, Pages 538-553]
Interval optimal control problems Optimal control of fractional differential equations with interval uncertainty [Volume 13, Issue 2, 2025, Pages 538-553]

J

Jacobi collocation method Jacobi collocation method for numerical solution of nonlinear weakly singular Volterra integro-differential equations: fractional and stochastic cases [Volume 13, Issue 3, 2025, Pages 742-757]
Jump-diffusion process Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]

K

K(2 Application of a new method for nonlinear partial differential equations of fractional order arising in fluid mechanics [Volume 13, Issue 1, 2025, Pages 1-12]
Kadomtsev-Petviashvili equation On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation [Volume 13, Issue 3, 2025, Pages 1022-1036]
KdV Application of a new method for nonlinear partial differential equations of fractional order arising in fluid mechanics [Volume 13, Issue 1, 2025, Pages 1-12]
Kernel density estimation Kernel density estimation applications in vessel extraction for MRA images [Volume 13, Issue 1, 2025, Pages 190-200]
Kernel functions A higher-order kernel approach for linear fourth-order boundary value problems [Volume 13, Issue 3, 2025, Pages 758-767]
Kirchhoff-double phase systems Some existence and nonexistence results for a class of Kirchhoff-double phase systems in bounded domains [Volume 13, Issue 3, 2025, Pages 839-849]

L

Lagrange polynomials Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method [Volume 13, Issue 2, 2025, Pages 479-493]
Lane-Emden equations An efficient high-order compact finite difference scheme for Lane-Emden-type equations [Volume 13, Issue 1, 2025, Pages 107-122]
Large-scale satellite images Comparison of feature-based algorithms for large-scale satellite image matching [Volume 13, Issue 1, 2025, Pages 142-156]
Least Deviations Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]
Legendre-Gauss-Radau pseudospectral methods Enhancing the Legendre-Gauss-Radau pseudospectral method with sigmoid-based control parameterization for solving bang-bang optimal control problems [Volume 13, Issue 3, 2025, Pages 802-814]
Lie symmetry analysis On the dynamics of newly generated analytical solutions and conserved vectors of a generalized 3D KP-BBM equation [Volume 13, Issue 2, 2025, Pages 682-708]
Limit cycle Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Linear fourth-order BVPs A higher-order kernel approach for linear fourth-order boundary value problems [Volume 13, Issue 3, 2025, Pages 758-767]
Linear quadratic regulator LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems [Volume 13, Issue 2, 2025, Pages 505-523]
Lipschitz condition Existence and uniqueness theorems for fractional differential equations with proportional delay [Volume 13, Issue 3, 2025, Pages 904-918]
Local M-fractional integral Solving a class of Volterra integral equations with M-derivative [Volume 13, Issue 1, 2025, Pages 282-293]
Lockdown Analysis of quarantine and liberate effects on viral infection using SEIR and Caputo $ lpha $-fractional-order model [Volume 13, Issue 3, 2025, Pages 768-782]
Lorenz model Analysis of a chaotic and a non-chaotic 3D dynamical system: the Quasi-Geostrophic omega equation and the Lorenz-96 model [Volume 13, Issue 3, 2025, Pages 721-741]
Lubich Generators A unified Explicit form for difference formulas for fractional and classical derivatives and applications [Volume 13, Issue 1, 2025, Pages 307-326]
Lukasiewicz semiring Dynamical systems in product Lukasiewicz semirings [Volume 13, Issue 2, 2025, Pages 676-681]
Lyapunov function Mathematical modeling of COVID-19 with a constant spatial diffusion term in Ghana [Volume 13, Issue 3, 2025, Pages 870-884]

M

Mathematical model Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]
Mathematical Modelling The use of technological intelligence model in solving terrorism dynamics: a case study of Nigeria [Volume 13, Issue 1, 2025, Pages 201-213]
Mathematical models Analysis of quarantine and liberate effects on viral infection using SEIR and Caputo $ lpha $-fractional-order model [Volume 13, Issue 3, 2025, Pages 768-782]
Measures of non-compactness Existence of solutions of Caputo fractional integro-differential equations [Volume 13, Issue 2, 2025, Pages 568-577]
Melnikov function Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Meshless local Petrov-Galerkin (MLPG) method Interpolating MLPG method to investigate predator-prey population dynamic with complex characters [Volume 13, Issue 2, 2025, Pages 357-372]
M-fractional Neumann method Solving a class of Volterra integral equations with M-derivative [Volume 13, Issue 1, 2025, Pages 282-293]
M-fractional Volterra integral equations Solving a class of Volterra integral equations with M-derivative [Volume 13, Issue 1, 2025, Pages 282-293]
Minimal Lagrangian Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times [Volume 13, Issue 1, 2025, Pages 249-257]
Minimax optimization On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem [Volume 13, Issue 3, 2025, Pages 1074-1084]
Mixed monotone operator q-Exponential fixed point theorem for mixed monotone operator with q-fractional problem [Volume 13, Issue 1, 2025, Pages 73-94]
Modified operational matrix A highly accurate wavelet approach for multi-term variable-order fractional multi-dimensional differential equations [Volume 13, Issue 3, 2025, Pages 850-869]
Moisture diffusivity Finite-difference method for Hygrothermoelastic boundary value problem [Volume 13, Issue 1, 2025, Pages 157-168]
Mott-fractional Mott functions Designing an efficient algorithm for fractional partial integro-differential viscoelastic equations with weakly singular kernel [Volume 13, Issue 1, 2025, Pages 214-232]
MRA images Kernel density estimation applications in vessel extraction for MRA images [Volume 13, Issue 1, 2025, Pages 190-200]
Multi-step DTM Multi-Step DTM simulation of Transesterification reactions model [Volume 13, Issue 2, 2025, Pages 634-645]
Müntz-Legendre wavelets On the numerical solution of the Bagley-Torvik equation using the M"{u}ntz-Legendre wavelet collocation method [Volume 13, Issue 3, 2025, Pages 968-979]
Musielak-Orliczspace Some existence and nonexistence results for a class of Kirchhoff-double phase systems in bounded domains [Volume 13, Issue 3, 2025, Pages 839-849]

N

Nano-channels A finite difference approach to solve the nonlinear model of electro-osmotic flow in nano-channels [Volume 13, Issue 3, 2025, Pages 919-926]
Newell-Whitehead-Segel Equation (NWS) On an efficient method for the fractional nonlinear Newell-Whithead-Segel equations [Volume 13, Issue 1, 2025, Pages 95-106]
Newtonian type linearization method (NTLM) On an efficient method for the fractional nonlinear Newell-Whithead-Segel equations [Volume 13, Issue 1, 2025, Pages 95-106]
Newton iterative algorithm A finite difference approach to solve the nonlinear model of electro-osmotic flow in nano-channels [Volume 13, Issue 3, 2025, Pages 919-926]
Newton Rephson method Numerical study of astrophysics equations using Bessel collocation methods of first Kind [Volume 13, Issue 2, 2025, Pages 466-478]
Nonlinear A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation [Volume 13, Issue 1, 2025, Pages 41-60]
Nonlinear algebraic system High-order numerical solution for a class of nonlinear Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 1059-1073]
Non-linear boundary value problem A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model [Volume 13, Issue 2, 2025, Pages 432-449]
Non-linear Klein-Gordon equation Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method [Volume 13, Issue 2, 2025, Pages 479-493]
Non-linear mathematical Mpox model Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
Nonlinear partial differential equation Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Nonlinear partial differential equations Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations [Volume 13, Issue 2, 2025, Pages 608-617]
Nonlinear partial differential equations Exploring high-frequency waves and soliton solutions of fluid turbulence through relaxation medium modeled by Vakhnenko-Parkes equation [Volume 13, Issue 2, 2025, Pages 646-658]
Nonlinear Schrödinger equation Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
Nonlinear Schrödinger equation (NLSE) Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media [Volume 13, Issue 1, 2025, Pages 271-281]
Nonlocal conditions A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Numerical simulation A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model [Volume 13, Issue 2, 2025, Pages 432-449]
Numerical solution Multi-Step DTM simulation of Transesterification reactions model [Volume 13, Issue 2, 2025, Pages 634-645]

O

ODEs Analysis of a chaotic and a non-chaotic 3D dynamical system: the Quasi-Geostrophic omega equation and the Lorenz-96 model [Volume 13, Issue 3, 2025, Pages 721-741]
Operational matrix A novel hybrid approach to approximate fractional sub-diffusion equation [Volume 13, Issue 2, 2025, Pages 420-431]
Operational matrix Solving a system of fractional Volterra integro-differential equations using cubic Hermit spline functions [Volume 13, Issue 3, 2025, Pages 980-994]
Optical solitons Extended hyperbolic function method for the model having cubic-quintic-septimal nonlinearity in weak nonlocal media [Volume 13, Issue 1, 2025, Pages 271-281]
Optimization method Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations [Volume 13, Issue 2, 2025, Pages 450-465]
Option pricing Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]
Order of Convergence High-order numerical solution for a class of nonlinear Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 1059-1073]
Ordinary differential equations Solving initial value problems using multilayer perceptron artificial neural networks [Volume 13, Issue 1, 2025, Pages 13-24]
Orthogonal collocation Numerical study of astrophysics equations using Bessel collocation methods of first Kind [Volume 13, Issue 2, 2025, Pages 466-478]

P

Parameters Analysis of the effect of isolation on the transmission dynamics of COVID-19: a mathematical modelling approach (R1) [Volume 13, Issue 1, 2025, Pages 123-141]
Partition Dynamical systems in product Lukasiewicz semirings [Volume 13, Issue 2, 2025, Pages 676-681]
Perturbation Control of fractional-order chaotic systems under perturbations [Volume 13, Issue 3, 2025, Pages 1037-1046]
Picard Fuch equations Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Picard’s iteration method A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Piecewise linear differential system Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Piecewise smooth differential system Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Poincare return map Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics [Volume 13, Issue 2, 2025, Pages 395-419]
Polytropic fluid Numerical study of astrophysics equations using Bessel collocation methods of first Kind [Volume 13, Issue 2, 2025, Pages 466-478]
Positive solution q-Exponential fixed point theorem for mixed monotone operator with q-fractional problem [Volume 13, Issue 1, 2025, Pages 73-94]
Predator-prey model Interpolating MLPG method to investigate predator-prey population dynamic with complex characters [Volume 13, Issue 2, 2025, Pages 357-372]
Prey Integrated pests management and food security: A mathematical analysis [Volume 13, Issue 2, 2025, Pages 524-537]
Prey-predator model Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior [Volume 13, Issue 1, 2025, Pages 294-306]
Prey-predator model A nonlinear mathematical model of the delayed predator-prey system that incorporates intraspecific predator competition and fear effect in prey [Volume 13, Issue 3, 2025, Pages 927-939]
Pseudo-spectral method Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method [Volume 13, Issue 2, 2025, Pages 479-493]

Q

Quadratic programming On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem [Volume 13, Issue 3, 2025, Pages 1074-1084]
Quasilinearization method A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Quasilinearization method An efficient high-order compact finite difference scheme for Lane-Emden-type equations [Volume 13, Issue 1, 2025, Pages 107-122]
Quasilinear Recurrence Equations Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]

R

Radial basis functions A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation [Volume 13, Issue 1, 2025, Pages 41-60]
Reaction-Diffusion model Mathematical modeling of COVID-19 with a constant spatial diffusion term in Ghana [Volume 13, Issue 3, 2025, Pages 870-884]
Relaxation Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Reproductive ratio Analysis of the effect of isolation on the transmission dynamics of COVID-19: a mathematical modelling approach (R1) [Volume 13, Issue 1, 2025, Pages 123-141]
Residuals Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]
Riesz derivative A method of lines for solving the nonlinear time- and space-fractional Schrödinger equation via stable Gaussian radial basis function interpolation [Volume 13, Issue 1, 2025, Pages 41-60]
RK4 method Multi-Step DTM simulation of Transesterification reactions model [Volume 13, Issue 2, 2025, Pages 634-645]
Rocks creeping Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
RqDTM Exploring novel solutions for the generalized q-deformed wave equation [Volume 13, Issue 2, 2025, Pages 554-567]

S

Semidefinite programming On the efficiency of the algorithm for solving complex quadratic double–ratio minimax optimization problem [Volume 13, Issue 3, 2025, Pages 1074-1084]
Sensitivity analysis Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative [Volume 13, Issue 2, 2025, Pages 494-504]
Sensitivity analysis Modelling the transmission of Mpox with a case study in Nigeria and the Democratic Republic of the Congo (DRC) [Volume 13, Issue 3, 2025, Pages 995-1011]
Separation method Exploring novel solutions for the generalized q-deformed wave equation [Volume 13, Issue 2, 2025, Pages 554-567]
Sequencing with one machine‎ A Hierarchical method to solve one machine multicriteria sequencing problem [Volume 13, Issue 1, 2025, Pages 327-338]
Shifted Gegenbauer polynomial Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method [Volume 13, Issue 3, 2025, Pages 815-827]
Shifted Grünwald approximation A unified Explicit form for difference formulas for fractional and classical derivatives and applications [Volume 13, Issue 1, 2025, Pages 307-326]
Sigmoid function Enhancing the Legendre-Gauss-Radau pseudospectral method with sigmoid-based control parameterization for solving bang-bang optimal control problems [Volume 13, Issue 3, 2025, Pages 802-814]
Simulation Analysis of the effect of isolation on the transmission dynamics of COVID-19: a mathematical modelling approach (R1) [Volume 13, Issue 1, 2025, Pages 123-141]
Simulation Integrated pests management and food security: A mathematical analysis [Volume 13, Issue 2, 2025, Pages 524-537]
Simulation and Discussion Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative [Volume 13, Issue 2, 2025, Pages 494-504]
Simulations A nonlinear mathematical model of the delayed predator-prey system that incorporates intraspecific predator competition and fear effect in prey [Volume 13, Issue 3, 2025, Pages 927-939]
Sinc-Galerkin method Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method [Volume 13, Issue 3, 2025, Pages 1047-1058]
Singular Perturbation Problems Fitted mesh cubic spline tension method for singularly perturbed delay differential equations with integral boundary condition [Volume 13, Issue 2, 2025, Pages 618-633]
Singular potential Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials [Volume 13, Issue 2, 2025, Pages 373-383]
Smoothing transformation Jacobi collocation method for numerical solution of nonlinear weakly singular Volterra integro-differential equations: fractional and stochastic cases [Volume 13, Issue 3, 2025, Pages 742-757]
Solitons and periodic structures Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Soliton solutions On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation [Volume 13, Issue 3, 2025, Pages 1022-1036]
Sparse matrix Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
Spatial spread Mathematical modeling of COVID-19 with a constant spatial diffusion term in Ghana [Volume 13, Issue 3, 2025, Pages 870-884]
Spectral collocation method A novel hybrid approach to approximate fractional sub-diffusion equation [Volume 13, Issue 2, 2025, Pages 420-431]
Spectral collocation method Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method [Volume 13, Issue 3, 2025, Pages 815-827]
Spherical Porous catalyst A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model [Volume 13, Issue 2, 2025, Pages 432-449]
Stability analysis Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem [Volume 13, Issue 2, 2025, Pages 578-591]
Stability analysis On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation [Volume 13, Issue 3, 2025, Pages 1022-1036]
Steady-state Reaction-Diffusion equation A new approximate analytical method for solving some non-linear boundary value problems in Reaction-Diffusion model [Volume 13, Issue 2, 2025, Pages 432-449]
Stochastic Jacobi collocation method for numerical solution of nonlinear weakly singular Volterra integro-differential equations: fractional and stochastic cases [Volume 13, Issue 3, 2025, Pages 742-757]
Stochastic interest rate Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]
Stochastic volatility Alternating direction implicit method for approximation solution of the HCIR model, including transaction costs in a Jump-Diffusion model [Volume 13, Issue 1, 2025, Pages 339-356]
Successive approximation method Existence and uniqueness theorems for fractional differential equations with proportional delay [Volume 13, Issue 3, 2025, Pages 904-918]
Sum of exponentials approximation Jacobi collocation method for numerical solution of nonlinear weakly singular Volterra integro-differential equations: fractional and stochastic cases [Volume 13, Issue 3, 2025, Pages 742-757]
Symmetries Symmetries of the minimal lagrangian hypersurfaces on cylindrically symmetric static space-times [Volume 13, Issue 1, 2025, Pages 249-257]

T

Technologtcal intelligence The use of technological intelligence model in solving terrorism dynamics: a case study of Nigeria [Volume 13, Issue 1, 2025, Pages 201-213]
Terrorism and Dynamics The use of technological intelligence model in solving terrorism dynamics: a case study of Nigeria [Volume 13, Issue 1, 2025, Pages 201-213]
Theorem of convergence Solving a class of Volterra integral equations with M-derivative [Volume 13, Issue 1, 2025, Pages 282-293]
Thermal diffusivity Finite-difference method for Hygrothermoelastic boundary value problem [Volume 13, Issue 1, 2025, Pages 157-168]
Three-point boundary value problem A Green’s function-based computationally efficient approach for solving a kind of nonlocal BVPs [Volume 13, Issue 1, 2025, Pages 25-40]
Time delay system LQR technique based SMC design for a class of uncertain time-delay Conic nonlinear systems [Volume 13, Issue 2, 2025, Pages 505-523]
Time-dependent Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]
Time-dependent deformation Flow of gas-condensate system in a time-dependent deformable reservoir with rock creep effect in the well Bottomhole zone [Volume 13, Issue 3, 2025, Pages 828-838]
Time fractional advection-diffusion equation Two-dimensional temporal fractional advection-diffusion problem resolved through the Sinc-Galerkin method [Volume 13, Issue 3, 2025, Pages 1047-1058]
Time fractional diffusion wave equation Numerical solving of multi-term time fractional diffusion-wave equations using shifted Gegenbauer spectral collocation method [Volume 13, Issue 3, 2025, Pages 815-827]
Time fractional Klein-Gordon equation A robust numerical method to find the solutions of time-fractional Klein-Gordon equation [Volume 13, Issue 2, 2025, Pages 709-720]
Time Series Solving the optimizing parameters problem for non-linear datasets using the high-order general least deviations method (GLDM) algorithm [Volume 13, Issue 3, 2025, Pages 940-967]
Transformation matrix A highly accurate wavelet approach for multi-term variable-order fractional multi-dimensional differential equations [Volume 13, Issue 3, 2025, Pages 850-869]
Traveling wave solution Soliton solutions to the DS and generalized DS system via an analytical method [Volume 13, Issue 1, 2025, Pages 233-248]
Traveling wave solution On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method [Volume 13, Issue 1, 2025, Pages 258-270]
Travelling Wave Solutions Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations [Volume 13, Issue 2, 2025, Pages 608-617]
Tumor-immune interaction Convergence analysis for piecewise Lagrange interpolation method of fractal fractional model of tumor-immune interaction with two different kernels [Volume 13, Issue 1, 2025, Pages 169-182]
Turing instability Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior [Volume 13, Issue 1, 2025, Pages 294-306]
Two-dimensional Numerical solution of the two-dimensional nonlinear schrödinger equation using an alternating direction implicit method [Volume 13, Issue 3, 2025, Pages 1012-1021]

V

Vakhnenko-Parkes equation Exploring high-frequency waves and soliton solutions of fluid turbulence through relaxation medium modeled by Vakhnenko-Parkes equation [Volume 13, Issue 2, 2025, Pages 646-658]
Variable-order fractional derivative A highly accurate wavelet approach for multi-term variable-order fractional multi-dimensional differential equations [Volume 13, Issue 3, 2025, Pages 850-869]
Variational technique Some existence and nonexistence results for a class of Kirchhoff-double phase systems in bounded domains [Volume 13, Issue 3, 2025, Pages 839-849]
VIM Exploring novel solutions for the generalized q-deformed wave equation [Volume 13, Issue 2, 2025, Pages 554-567]

W

Wavelet collocation method On the numerical solution of the Bagley-Torvik equation using the M"{u}ntz-Legendre wavelet collocation method [Volume 13, Issue 3, 2025, Pages 968-979]
Wavelet Galerkin method On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations [Volume 13, Issue 3, 2025, Pages 885-903]
Wave speed Mathematical modeling of COVID-19 with a constant spatial diffusion term in Ghana [Volume 13, Issue 3, 2025, Pages 870-884]

Z

Zakharov-Kuznetsov Application of a new method for nonlinear partial differential equations of fractional order arising in fluid mechanics [Volume 13, Issue 1, 2025, Pages 1-12]
Zakharov–Kuznetsov equation On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method [Volume 13, Issue 1, 2025, Pages 258-270]

Keyword Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

V

W

Z