Computational Methods for Differential Equations

A

Abel’s equation Solving Abel’s equations with the shifted Legendre polynomials [Volume 11, Issue 4, 2023, Pages 865-875]
ABS Algorithm An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions [Volume 11, Issue 1, 2023, Pages 143-160]
Adaptive Runge-Kutta Method A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation [Volume 11, Issue 1, 2023, Pages 130-142]
Adomian Decomposition Method Solution of time-fractional equations via Sumudu-Adomian decomposition method [Volume 11, Issue 2, 2023, Pages 345-356]
Algebraic equations Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]
Analytical solution A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He's Frequency-Amplitude formulation [Volume 11, Issue 3, 2023, Pages 464-477]
Ananthaswamy-Sivasankari method (ASM) A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid [Volume 11, Issue 4, 2023, Pages 696-715]
Approximately invariant solution Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation [Volume 11, Issue 1, 2023, Pages 175-182]
Approximate Moving Least Squares Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation [Volume 11, Issue 1, 2023, Pages 108-129]
Approximate symmetry Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation [Volume 11, Issue 1, 2023, Pages 175-182]
Approximation Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions [Volume 11, Issue 1, 2023, Pages 32-41]
Asymptotic behaviour Numerical computation of exponential functions in frame of Nabla fractional calculus [Volume 11, Issue 2, 2023, Pages 291-302]
Asymtotic stability Linear B-spline finite element Method for solving delay reaction diffusion equation [Volume 11, Issue 1, 2023, Pages 161-174]

B

Bakhvalov-Shishkin mesh A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation [Volume 11, Issue 4, 2023, Pages 822-833]
Bezier curves Improved residual method for approximating Bratu problem [Volume 11, Issue 3, 2023, Pages 535-547]
Boundary layer A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts [Volume 11, Issue 1, 2023, Pages 42-51]
Boundary value problem A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions [Volume 11, Issue 2, 2023, Pages 241-253]
Boundary value problem To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition [Volume 11, Issue 2, 2023, Pages 332-344]
Boundary value problem Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method [Volume 11, Issue 3, 2023, Pages 643-663]
Boundary value problems Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Boundary value problems Non-polynomial cubic spline method for solution of higher order boundary value problems [Volume 11, Issue 2, 2023, Pages 225-240]
Bratu equations Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Bratu Problem Improved residual method for approximating Bratu problem [Volume 11, Issue 3, 2023, Pages 535-547]
B-Spline A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline [Volume 11, Issue 1, 2023, Pages 95-107]

C

Caputo-derivative Solution of time-fractional equations via Sumudu-Adomian decomposition method [Volume 11, Issue 2, 2023, Pages 345-356]
Caputo differential operator Solving Abel’s equations with the shifted Legendre polynomials [Volume 11, Issue 4, 2023, Pages 865-875]
Caputo-Fabrizio operator Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations [Volume 11, Issue 3, 2023, Pages 440-463]
Caputo fractional derivative Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions [Volume 11, Issue 1, 2023, Pages 32-41]
Caputo fractional derivative On approximating eigenvalues and eigenfunctions of fractional order Sturm-Liouville problems [Volume 11, Issue 4, 2023, Pages 811-821]
Caputo fractional derivative To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition [Volume 11, Issue 2, 2023, Pages 332-344]
Chaotic System Optimal fractional order PID controller performance in chaotic system of HIV disease: particle swarm and genetic algorithms optimization method [Volume 11, Issue 2, 2023, Pages 207-224]
Chebyshev cardinal wavelets An efficient numerical approach for solving nonlinear Volterra integral equations [Volume 11, Issue 3, 2023, Pages 615-629]
Collocation method Numerical solution of space-time fractional PDEs with variable coefficients using shifted Jacobi collocation method [Volume 11, Issue 1, 2023, Pages 81-94]
Collocation method A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline [Volume 11, Issue 1, 2023, Pages 95-107]
Collocation method Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations [Volume 11, Issue 3, 2023, Pages 589-604]
Collocation points Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]
Compact discretization Infinitely smooth multiquadric RBFs combined high-resolution compact discretization for nonlinear 2D elliptic PDEs on a scattered grid network [Volume 11, Issue 4, 2023, Pages 753-775]
Compressibility Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects [Volume 11, Issue 4, 2023, Pages 664-675]
Conformable derivative Analytical solutions of the fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation [Volume 11, Issue 3, 2023, Pages 564-575]
Conservation laws Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation [Volume 11, Issue 2, 2023, Pages 399-411]
Contaminant transport Contaminant transportation modeling with time dependent dispersion [Volume 11, Issue 3, 2023, Pages 605-614]
Convergence Linear B-spline finite element Method for solving delay reaction diffusion equation [Volume 11, Issue 1, 2023, Pages 161-174]
Convergence A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations [Volume 11, Issue 2, 2023, Pages 357-368]
Convergence Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method [Volume 11, Issue 3, 2023, Pages 643-663]
Convergence A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach [Volume 11, Issue 4, 2023, Pages 716-726]
Convergence analysis Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations [Volume 11, Issue 1, 2023, Pages 183-196]
Convergence analysis Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Convergence analysis Non-polynomial cubic spline method for solution of higher order boundary value problems [Volume 11, Issue 2, 2023, Pages 225-240]
Convergence analysis Numerical methods for m-polar fuzzy initial value problems [Volume 11, Issue 3, 2023, Pages 412-439]
Coupled Burger’s equation A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation [Volume 11, Issue 1, 2023, Pages 130-142]
Cox-Ingersoll and Ross model Numerical solution of stochastic models using spectral collocation method [Volume 11, Issue 3, 2023, Pages 630-642]
Crank Nicolson Linear B-spline finite element Method for solving delay reaction diffusion equation [Volume 11, Issue 1, 2023, Pages 161-174]
Cross diffusion Steady state bifurcation in a cross diffusion prey-predator model [Volume 11, Issue 2, 2023, Pages 254-262]
Cross product Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations [Volume 11, Issue 3, 2023, Pages 440-463]

D

Darcy-Forchheimer nanofluid flow A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid [Volume 11, Issue 4, 2023, Pages 696-715]
Deformation Mathematical modeling of a nonlinear two-phase flow in a porous medium and the inflow of volatile oil to a well taking into account inertial effects [Volume 11, Issue 4, 2023, Pages 664-675]
Delay reaction diffusion equation Linear B-spline finite element Method for solving delay reaction diffusion equation [Volume 11, Issue 1, 2023, Pages 161-174]
Dickson polynomials Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]
Differential equation On the existence of periodic solutions of third order delay differential equations [Volume 11, Issue 2, 2023, Pages 319-331]
Differential invariants Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation [Volume 11, Issue 2, 2023, Pages 399-411]
Differential invariants A finite generating set of differential invariants for Lie symmetry group of the fifth-order KdV types [Volume 11, Issue 4, 2023, Pages 803-810]
Differential quadrature method Numerical solution of nonlinear Sine-Gordon equation using modified cubic B-spline-based differential quadrature method [Volume 11, Issue 2, 2023, Pages 369-386]
Duffing equation A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions [Volume 11, Issue 2, 2023, Pages 241-253]

E

EBM A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He's Frequency-Amplitude formulation [Volume 11, Issue 3, 2023, Pages 464-477]
Efficient Algorithm A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He's Frequency-Amplitude formulation [Volume 11, Issue 3, 2023, Pages 464-477]
Eigenfunction On approximating eigenvalues and eigenfunctions of fractional order Sturm-Liouville problems [Volume 11, Issue 4, 2023, Pages 811-821]
Error analysis Improved residual method for approximating Bratu problem [Volume 11, Issue 3, 2023, Pages 535-547]
Error analysis A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease [Volume 11, Issue 4, 2023, Pages 834-850]
Error estimation Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]
European option Haar wavelet-based valuation method for pricing European options [Volume 11, Issue 2, 2023, Pages 281-290]
Exact solution A novel scheme for SMCH equation with two different approaches [Volume 11, Issue 2, 2023, Pages 263-280]
Existence and uniqueness To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition [Volume 11, Issue 2, 2023, Pages 332-344]
Exponential function Numerical computation of exponential functions in frame of Nabla fractional calculus [Volume 11, Issue 2, 2023, Pages 291-302]
Exp(-φ(ξ))-expansion method Analytical solutions of the fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation [Volume 11, Issue 3, 2023, Pages 564-575]
Extra distributed-order fractional derivative operator An optimum solution for multi-dimensional distributed-order fractional differential equations [Volume 11, Issue 3, 2023, Pages 548-563]
Extrapolation methods Extrapolated triangular splitting method to interval system of linear algebraic equations [Volume 11, Issue 4, 2023, Pages 738-752]
Extremal solutions Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions [Volume 11, Issue 1, 2023, Pages 32-41]

F

Fitted Mesh scheme Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition [Volume 11, Issue 3, 2023, Pages 478-494]
Fixed point Existence of nonoscillatory solutions of second-order differential equations with mixed neutral term [Volume 11, Issue 4, 2023, Pages 851-864]
Fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation Analytical solutions of the fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation [Volume 11, Issue 3, 2023, Pages 564-575]
Fractional ABC-derivative A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease [Volume 11, Issue 4, 2023, Pages 834-850]
Fractional Fokker-Planck equations(STF-FPE)‎ New approximations of space-time fractional Fokker-Planck equations [Volume 11, Issue 3, 2023, Pages 495-521]
Fractional-order Fibonacci functions An optimum solution for multi-dimensional distributed-order fractional differential equations [Volume 11, Issue 3, 2023, Pages 548-563]
Free boundary problem Numerical solution of one-phase Stefan problem for the non-classical heat equation with a convective condition [Volume 11, Issue 4, 2023, Pages 776-784]
Fuzzy function A method for second-order linear fuzzy two-point boundary value problems based on the Hukuhara differentiability [Volume 11, Issue 3, 2023, Pages 576-588]
Fuzzy number A method for second-order linear fuzzy two-point boundary value problems based on the Hukuhara differentiability [Volume 11, Issue 3, 2023, Pages 576-588]
Fuzzy two-point boundary value problems A method for second-order linear fuzzy two-point boundary value problems based on the Hukuhara differentiability [Volume 11, Issue 3, 2023, Pages 576-588]

G

Gaussian noise Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Gelfand-Bratu equation Infinitely smooth multiquadric RBFs combined high-resolution compact discretization for nonlinear 2D elliptic PDEs on a scattered grid network [Volume 11, Issue 4, 2023, Pages 753-775]
General decay stability Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Generalized (G′/G)-expansion method Analytical solutions of the fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation [Volume 11, Issue 3, 2023, Pages 564-575]
Generalized Hukuhara derivative Numerical methods for m-polar fuzzy initial value problems [Volume 11, Issue 3, 2023, Pages 412-439]
Genral stock model Numerical solution of stochastic models using spectral collocation method [Volume 11, Issue 3, 2023, Pages 630-642]
Gyrotactic Microorganisms A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid [Volume 11, Issue 4, 2023, Pages 696-715]

H

Haar wavelet Haar wavelet-based valuation method for pricing European options [Volume 11, Issue 2, 2023, Pages 281-290]
HAFF A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He's Frequency-Amplitude formulation [Volume 11, Issue 3, 2023, Pages 464-477]
Higher-order Non-polynomial cubic spline method for solution of higher order boundary value problems [Volume 11, Issue 2, 2023, Pages 225-240]
Higher order Boussinesq equation Multi-Soliton Solutions to the Generalized Boussinesq Equation of Tenth Order [Volume 11, Issue 4, 2023, Pages 727-737]
High order fractional differential equation To study existence of unique solution and numerically solving for a kind of three-point boundary fractional high-order problem subject to Robin condition [Volume 11, Issue 2, 2023, Pages 332-344]
HIV Optimal fractional order PID controller performance in chaotic system of HIV disease: particle swarm and genetic algorithms optimization method [Volume 11, Issue 2, 2023, Pages 207-224]
Holder estimates Holder estimates of solutions degenerate nonlinear parabolic equations [Volume 11, Issue 1, 2023, Pages 197-206]
Hukuhara differentiability A method for second-order linear fuzzy two-point boundary value problems based on the Hukuhara differentiability [Volume 11, Issue 3, 2023, Pages 576-588]
Hybrid functions Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations [Volume 11, Issue 1, 2023, Pages 183-196]
Hybrid functions Jacobi wavelets method for numerical solution of fractional population growth model [Volume 11, Issue 2, 2023, Pages 387-398]
Hybrid functions A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions [Volume 11, Issue 2, 2023, Pages 241-253]
Hybrid scheme A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation [Volume 11, Issue 4, 2023, Pages 822-833]

I

Initial value problem Numerical methods for m-polar fuzzy initial value problems [Volume 11, Issue 3, 2023, Pages 412-439]
Initial value problem Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations [Volume 11, Issue 3, 2023, Pages 440-463]
Integral Boundary Condition Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition [Volume 11, Issue 3, 2023, Pages 478-494]
Integral boundary conditions A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions [Volume 11, Issue 2, 2023, Pages 241-253]
Integral equation An efficient numerical approach for solving nonlinear Volterra integral equations [Volume 11, Issue 3, 2023, Pages 615-629]
Integral equation Solving Abel’s equations with the shifted Legendre polynomials [Volume 11, Issue 4, 2023, Pages 865-875]
Interval systems of linear algebraic equations Extrapolated triangular splitting method to interval system of linear algebraic equations [Volume 11, Issue 4, 2023, Pages 738-752]
Inverse problem An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions [Volume 11, Issue 1, 2023, Pages 143-160]

J

Jacobi polynomials Numerical solution of space-time fractional PDEs with variable coefficients using shifted Jacobi collocation method [Volume 11, Issue 1, 2023, Pages 81-94]
Jacobi polynomials Jacobi wavelets method for numerical solution of fractional population growth model [Volume 11, Issue 2, 2023, Pages 387-398]

K

Kaucher interval arithmetic Extrapolated triangular splitting method to interval system of linear algebraic equations [Volume 11, Issue 4, 2023, Pages 738-752]
Kawaharara equation A finite generating set of differential invariants for Lie symmetry group of the fifth-order KdV types [Volume 11, Issue 4, 2023, Pages 803-810]
KdV equation A numerical method for KdV equation using rational radial basis functions [Volume 11, Issue 2, 2023, Pages 303-318]
KdV equations A finite generating set of differential invariants for Lie symmetry group of the fifth-order KdV types [Volume 11, Issue 4, 2023, Pages 803-810]
Khasiminskii condition A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients [Volume 11, Issue 3, 2023, Pages 522-534]
Klein-Gordon equation of fractional order Solution of time-fractional equations via Sumudu-Adomian decomposition method [Volume 11, Issue 2, 2023, Pages 345-356]

L

Laplace transform variational iteration method Contaminant transportation modeling with time dependent dispersion [Volume 11, Issue 3, 2023, Pages 605-614]
Leave-One-Out Cross Validation Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation [Volume 11, Issue 1, 2023, Pages 108-129]
Leave-Two-Out Cross Validation Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation [Volume 11, Issue 1, 2023, Pages 108-129]
Legendre polynomials A numerical method for solving the Duffing equation involving both integral and non-integral forcing terms with separated and integral boundary conditions [Volume 11, Issue 2, 2023, Pages 241-253]
Levy noise Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Lie-Trotter splitting A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline [Volume 11, Issue 1, 2023, Pages 95-107]
Linear B-spline Linear B-spline finite element Method for solving delay reaction diffusion equation [Volume 11, Issue 1, 2023, Pages 161-174]
Linear fuzzy differential equations Fully fuzzy initial value problem of Caputo-Fabrizio fractional differential equations [Volume 11, Issue 3, 2023, Pages 440-463]
LKF On the existence of periodic solutions of third order delay differential equations [Volume 11, Issue 2, 2023, Pages 319-331]
Local Lipschitz condition A modi fied split-step truncated Euler-Maruyama method for SDEs with non-globally Lipschitz continuous coefficients [Volume 11, Issue 3, 2023, Pages 522-534]
Lucas polynomials Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Lumped Galerkin method A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline [Volume 11, Issue 1, 2023, Pages 95-107]

M

Markovian jumps systems Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Mathematical Model of COVID-19 A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease [Volume 11, Issue 4, 2023, Pages 834-850]
Mittag-Leffler Kernel A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease [Volume 11, Issue 4, 2023, Pages 834-850]
Modified cubic B-spline Numerical solution of nonlinear Sine-Gordon equation using modified cubic B-spline-based differential quadrature method [Volume 11, Issue 2, 2023, Pages 369-386]
Modified Homotopy analysis method (MHAM) A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid [Volume 11, Issue 4, 2023, Pages 696-715]
Modified Kudryashov method Analytical solutions of the fractional (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation [Volume 11, Issue 3, 2023, Pages 564-575]
Moving frame Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation [Volume 11, Issue 2, 2023, Pages 399-411]
Moving frames A finite generating set of differential invariants for Lie symmetry group of the fifth-order KdV types [Volume 11, Issue 4, 2023, Pages 803-810]
Moving least squares method A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach [Volume 11, Issue 4, 2023, Pages 716-726]
Multi-Order Fractional differential equation A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease [Volume 11, Issue 4, 2023, Pages 834-850]

N

Nabla fractional difference Numerical computation of exponential functions in frame of Nabla fractional calculus [Volume 11, Issue 2, 2023, Pages 291-302]
Navier-Stokes equation A third-order weighted essentially non-oscillatory-flux limiter scheme for two-dimensional incompressible Navier-Stokes equations [Volume 11, Issue 1, 2023, Pages 1-11]
Neural Networks Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Neutral differential equations Existence of nonoscillatory solutions of second-order differential equations with mixed neutral term [Volume 11, Issue 4, 2023, Pages 851-864]
Neutral-type systems Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Newton’s law of cooling equation Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay [Volume 11, Issue 4, 2023, Pages 785-802]
Non-classical Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method [Volume 11, Issue 3, 2023, Pages 643-663]
Non-globally Lipschitz conditions An explicit split-step truncated Milstein method for stochastic differential equations [Volume 11, Issue 4, 2023, Pages 676-695]
Nonlinear Holder estimates of solutions degenerate nonlinear parabolic equations [Volume 11, Issue 1, 2023, Pages 197-206]
Non-linear Non-polynomial cubic spline method for solution of higher order boundary value problems [Volume 11, Issue 2, 2023, Pages 225-240]
Nonlinear boundary conditions Extremal solutions for multi-term nonlinear fractional differential equations with nonlinear boundary conditions [Volume 11, Issue 1, 2023, Pages 32-41]
Nonlinear Fredholm-Volterra integral equation Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations [Volume 11, Issue 1, 2023, Pages 183-196]
Nonlinear Klein-Gordon and sine-Gordon equations A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations [Volume 11, Issue 2, 2023, Pages 357-368]
Nonlinear Klein-Gordon equation Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation [Volume 11, Issue 2, 2023, Pages 399-411]
Nonlinear Oscillators A novel analytical approximation approach for strongly nonlinear oscillation systems based on the energy balance method and He's Frequency-Amplitude formulation [Volume 11, Issue 3, 2023, Pages 464-477]
Nonlinear Pantograph Equations Spectral collocation method based on special functions for solving nonlinear high-order pantograph equations [Volume 11, Issue 3, 2023, Pages 589-604]
Non-linear parabolic partial differential equation A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation [Volume 11, Issue 1, 2023, Pages 130-142]
Nonoscillatory solution Existence of nonoscillatory solutions of second-order differential equations with mixed neutral term [Volume 11, Issue 4, 2023, Pages 851-864]
Non-polynomial spline Non-polynomial cubic spline method for solution of higher order boundary value problems [Volume 11, Issue 2, 2023, Pages 225-240]

O

Operational matrices Numerical solution of space-time fractional PDEs with variable coefficients using shifted Jacobi collocation method [Volume 11, Issue 1, 2023, Pages 81-94]
Operational matrix Jacobi wavelets method for numerical solution of fractional population growth model [Volume 11, Issue 2, 2023, Pages 387-398]
Operational matrix Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Operational matrix An efficient numerical approach for solving nonlinear Volterra integral equations [Volume 11, Issue 3, 2023, Pages 615-629]
Optimal control problem Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]
Optimal Fractional Order Controller Optimal fractional order PID controller performance in chaotic system of HIV disease: particle swarm and genetic algorithms optimization method [Volume 11, Issue 2, 2023, Pages 207-224]
Optimal system Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation [Volume 11, Issue 1, 2023, Pages 175-182]
Optimization method An optimum solution for multi-dimensional distributed-order fractional differential equations [Volume 11, Issue 3, 2023, Pages 548-563]
Option pricing Haar wavelet-based valuation method for pricing European options [Volume 11, Issue 2, 2023, Pages 281-290]

P

Particle swarm optimization algorithm Optimal fractional order PID controller performance in chaotic system of HIV disease: particle swarm and genetic algorithms optimization method [Volume 11, Issue 2, 2023, Pages 207-224]
Perturbed mKdV-KS equation Approximate symmetry group analysis and similarity reductions of the perturbed mKdV-KS equation [Volume 11, Issue 1, 2023, Pages 175-182]
Population growth model Jacobi wavelets method for numerical solution of fractional population growth model [Volume 11, Issue 2, 2023, Pages 387-398]
Prey-predator model Steady state bifurcation in a cross diffusion prey-predator model [Volume 11, Issue 2, 2023, Pages 254-262]
Pseudospectral method A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations [Volume 11, Issue 2, 2023, Pages 357-368]

Q

Quintic B-spline A new numerical algorithm based on Quintic B-Spline and adaptive time integrator for Coupled Burger’s equation [Volume 11, Issue 1, 2023, Pages 130-142]

R

Radial basis function Infinitely smooth multiquadric RBFs combined high-resolution compact discretization for nonlinear 2D elliptic PDEs on a scattered grid network [Volume 11, Issue 4, 2023, Pages 753-775]
Radial basis functions Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation [Volume 11, Issue 1, 2023, Pages 108-129]
RBF A numerical method for KdV equation using rational radial basis functions [Volume 11, Issue 2, 2023, Pages 303-318]
Reaction-Diffusion Problem An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions [Volume 11, Issue 1, 2023, Pages 143-160]
Regularization An ABC algorithm based approach to solve a nonlinear inverse reaction-diffusion problem associate with the ecological invasions [Volume 11, Issue 1, 2023, Pages 143-160]
Residual method Improved residual method for approximating Bratu problem [Volume 11, Issue 3, 2023, Pages 535-547]
Runge-Kutta method A numerical method for KdV equation using rational radial basis functions [Volume 11, Issue 2, 2023, Pages 303-318]

S

Scattered grid network Infinitely smooth multiquadric RBFs combined high-resolution compact discretization for nonlinear 2D elliptic PDEs on a scattered grid network [Volume 11, Issue 4, 2023, Pages 753-775]
Schrodinger equation Infinitely smooth multiquadric RBFs combined high-resolution compact discretization for nonlinear 2D elliptic PDEs on a scattered grid network [Volume 11, Issue 4, 2023, Pages 753-775]
Shape Parameter Choosing the best value of shape parameter in radial basis functions by Leave-P-Out Cross Validation [Volume 11, Issue 1, 2023, Pages 108-129]
Shifted Legendre polynomial Solving Abel’s equations with the shifted Legendre polynomials [Volume 11, Issue 4, 2023, Pages 865-875]
Sinc Collocation method Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method [Volume 11, Issue 3, 2023, Pages 643-663]
Sinc operational matrices A pseudospectral Sinc method for numerical investigation of the nonlinear time-fractional Klein-Gordon and sine-Gordon equations [Volume 11, Issue 2, 2023, Pages 357-368]
Sine-Gordon equation Numerical solution of nonlinear Sine-Gordon equation using modified cubic B-spline-based differential quadrature method [Volume 11, Issue 2, 2023, Pages 369-386]
Singular initial value problems Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Singularly perturbed problems Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition [Volume 11, Issue 3, 2023, Pages 478-494]
Singular perturbation A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts [Volume 11, Issue 1, 2023, Pages 42-51]
Singular perturbation A second order numerical scheme for solving mixed type boundary value problems involving singular perturbation [Volume 11, Issue 4, 2023, Pages 822-833]
SMCH equation A novel scheme for SMCH equation with two different approaches [Volume 11, Issue 2, 2023, Pages 263-280]
Spectral methods Modified Lucas polynomials for the numerical treatment of second-order boundary value problems [Volume 11, Issue 1, 2023, Pages 12-31]
Split-step methods An explicit split-step truncated Milstein method for stochastic differential equations [Volume 11, Issue 4, 2023, Pages 676-695]
SSP-RK54 Numerical solution of nonlinear Sine-Gordon equation using modified cubic B-spline-based differential quadrature method [Volume 11, Issue 2, 2023, Pages 369-386]
Stability A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach [Volume 11, Issue 4, 2023, Pages 716-726]
Steady state bifurcation Steady state bifurcation in a cross diffusion prey-predator model [Volume 11, Issue 2, 2023, Pages 254-262]
Stochastic differential equations An explicit split-step truncated Milstein method for stochastic differential equations [Volume 11, Issue 4, 2023, Pages 676-695]
Strong convergence rate An explicit split-step truncated Milstein method for stochastic differential equations [Volume 11, Issue 4, 2023, Pages 676-695]
Sturm-Liouville problem On approximating eigenvalues and eigenfunctions of fractional order Sturm-Liouville problems [Volume 11, Issue 4, 2023, Pages 811-821]
Sumudu transform Solution of time-fractional equations via Sumudu-Adomian decomposition method [Volume 11, Issue 2, 2023, Pages 345-356]
Symbolic computation A novel scheme for SMCH equation with two different approaches [Volume 11, Issue 2, 2023, Pages 263-280]
Syzygy Applying moving frames to finding conservation laws of the nonlinear Klein-Gordon equation [Volume 11, Issue 2, 2023, Pages 399-411]

T

Taylor expansion Numerical methods for m-polar fuzzy initial value problems [Volume 11, Issue 3, 2023, Pages 412-439]
The Hirota bilinear method Multi-Soliton Solutions to the Generalized Boussinesq Equation of Tenth Order [Volume 11, Issue 4, 2023, Pages 727-737]
The MEW equation A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline [Volume 11, Issue 1, 2023, Pages 95-107]
The spectral collocation method based on radial basis functions Numerical solution of stochastic models using spectral collocation method [Volume 11, Issue 3, 2023, Pages 630-642]
The $tanh$ method Multi-Soliton Solutions to the Generalized Boussinesq Equation of Tenth Order [Volume 11, Issue 4, 2023, Pages 727-737]
Third-order Numerical solution of third-Order boundary value problems using non-classical sinc-collocation method [Volume 11, Issue 3, 2023, Pages 643-663]
Time delay parabolic problem A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems involving mixed space shifts [Volume 11, Issue 1, 2023, Pages 42-51]
Time-Fractional Telegraph Equation A numerical approximation for the solution of a time-fractional telegraph equation by the moving least squares approach [Volume 11, Issue 4, 2023, Pages 716-726]
Time-varying delays Stability for neutral-type integro-differential neural networks with random switches in noise and delay [Volume 11, Issue 1, 2023, Pages 65-80]
Truncated Milstein method An explicit split-step truncated Milstein method for stochastic differential equations [Volume 11, Issue 4, 2023, Pages 676-695]

U

UNO limiter A third-order weighted essentially non-oscillatory-flux limiter scheme for two-dimensional incompressible Navier-Stokes equations [Volume 11, Issue 1, 2023, Pages 1-11]

V

Vasicek Model Numerical solution of stochastic models using spectral collocation method [Volume 11, Issue 3, 2023, Pages 630-642]
Viscous dissipation A mathematical study on non-linear ordinary differential equation for Magnetohydrodynamic flow of the Darcy-Forchheimer nanofluid [Volume 11, Issue 4, 2023, Pages 696-715]
Volterra integro-differential equation Optimal control of Volterra integro-differential equations based on interpolation polynomials and collocation method [Volume 11, Issue 1, 2023, Pages 52-64]

W

Wavelets Jacobi wavelets method for numerical solution of fractional population growth model [Volume 11, Issue 2, 2023, Pages 387-398]
Weakly singular kernel Hybrid collocation method for some classes of second-kind nonlinear weakly singular integral equations [Volume 11, Issue 1, 2023, Pages 183-196]
WENO A third-order weighted essentially non-oscillatory-flux limiter scheme for two-dimensional incompressible Navier-Stokes equations [Volume 11, Issue 1, 2023, Pages 1-11]

Keyword Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W