Computational Methods for Differential Equations

Keyword Index

A

Adaptive Moving Mesh A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth [Volume 9, Issue 2, 2021, Pages 327-346]
Adaptive Neuro-Fuzzy Inference System Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Alpert‎ ‎wavelet system Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations [Volume 9, Issue 3, 2021, Pages 762-773]
American option A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]
Ansatz method New exact solutions and numerical approximations of the generalized KdV equation [Volume 9, Issue 3, 2021, Pages 670-691]
Approximate solution Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations [Volume 9, Issue 3, 2021, Pages 846-857]
Asymptotic Adomian decomposition method Asymptotic decomposition method for fractional order Riccati differential equation [Volume 9, Issue 1, 2021, Pages 63-78]
Avascular Tumor Growth A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth [Volume 9, Issue 2, 2021, Pages 327-346]

B

Banach Space Analytical solution for descriptor system in partial differential equations [Volume 9, Issue 2, 2021, Pages 467-479]
Basic reproduction number A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]
Bernoulli operational matrix A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components [Volume 9, Issue 2, 2021, Pages 446-466]
Bernoulli wavelets Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations [Volume 9, Issue 3, 2021, Pages 846-857]
Bifurcation A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]
Block-pulse wavelet Numerical analysis of fractional differential equation by TSI-wavelet method [Volume 9, Issue 3, 2021, Pages 659-669]
Blow-up Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay [Volume 9, Issue 2, 2021, Pages 623-636]
Bogdanov-Takens bifurcation Global dynamics and numerical bifurcation of a bioeconomic system [Volume 9, Issue 2, 2021, Pages 427-445]
Boundary value problem Second order boundary value problems of nonsingular type on time scales [Volume 9, Issue 4, 2021, Pages 1214-1222]
Boundary value problem(BVP) Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Bounds Bounds of Riemann-Liouville fractional integral operators [Volume 9, Issue 2, 2021, Pages 637-648]
Brusselator model Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system [Volume 9, Issue 2, 2021, Pages 358-374]
B-Spline Application of cubic B-spline collocation method for reaction diffusion Fisher's equation [Volume 9, Issue 1, 2021, Pages 22-35]

C

Caffarelli-Kohn-Nirenberg inequalities Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities [Volume 9, Issue 2, 2021, Pages 589-603]
Caputo derivative Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process [Volume 9, Issue 1, 2021, Pages 258-272]
Caputo derivative Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations [Volume 9, Issue 3, 2021, Pages 858-873]
Caputo factional derivative Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Caputo fractional derivative Asymptotic decomposition method for fractional order Riccati differential equation [Volume 9, Issue 1, 2021, Pages 63-78]
Caputo fractional derivative On the existence of positive solutions for a non-autonomous fractional differential equation with integral boundary conditions [Volume 9, Issue 1, 2021, Pages 36-51]
Caputo fractional derivative Solving fractional optimal control problems using Genocchi polynomials [Volume 9, Issue 1, 2021, Pages 79-93]
Caputo fractional derivative Conformable double Laplace transform method for solving conformable fractional partial differential equations [Volume 9, Issue 3, 2021, Pages 908-918]
CEV model A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]
Characterization theorem Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Chebyshev polynomials Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations [Volume 9, Issue 3, 2021, Pages 858-873]
Collocation Application of cubic B-spline collocation method for reaction diffusion Fisher's equation [Volume 9, Issue 1, 2021, Pages 22-35]
Collocation An exponential cubic B-spline algorithm for solving the nonlinear Coupled Burgers’ equation [Volume 9, Issue 4, 2021, Pages 1109-1127]
Collocation method A Laguerre approach for solving of the systems of linear differential equations and residual improvement [Volume 9, Issue 2, 2021, Pages 553-576]
Collocation method Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations [Volume 9, Issue 3, 2021, Pages 858-873]
Collocation method Laguerre collocation method for solving Lane-Emden type equations [Volume 9, Issue 4, 2021, Pages 1176-1197]
Collocation method An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions [Volume 9, Issue 4, 2021, Pages 1198-1213]
Collocation points A Laguerre approach for solving of the systems of linear differential equations and residual improvement [Volume 9, Issue 2, 2021, Pages 553-576]
Combined Hirota-Lakshmanan-Porsezian-Daniel equation Exact solutions of the combined Hirota-LPD equation with variable coefficients [Volume 9, Issue 1, 2021, Pages 94-116]
Compact difference scheme A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]
Compatibility method Generalized symmetries and conservation laws of (3+1)-dimensional variable coefficient Zakharov-Kuznetsov equation [Volume 9, Issue 1, 2021, Pages 300-312]
Conformable fractional derivative (CFD) Conformable double Laplace transform method for solving conformable fractional partial differential equations [Volume 9, Issue 3, 2021, Pages 908-918]
Conservation laws Generalized symmetries and conservation laws of (3+1)-dimensional variable coefficient Zakharov-Kuznetsov equation [Volume 9, Issue 1, 2021, Pages 300-312]
Constraint qualification Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints [Volume 9, Issue 2, 2021, Pages 347-357]
Control Sensitivity analytic and synchronization of a new fractional-order financial system [Volume 9, Issue 3, 2021, Pages 788-798]
Controllability Approximate distributed controllability of nonlocal Rayleigh beam [Volume 9, Issue 1, 2021, Pages 180-186]
Control parameterization An efficient numerical solution for time switching optimal control problems [Volume 9, Issue 1, 2021, Pages 225-243]
Convergence Regularization of a nonlinear inverse problem by discrete mollification‎ ‎method [Volume 9, Issue 1, 2021, Pages 313-326]
Convergence A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components [Volume 9, Issue 2, 2021, Pages 446-466]
Convergence On the numerical treatment and analysis of Hammerstein integral equation [Volume 9, Issue 2, 2021, Pages 493-510]
Convergence analysis An efficient technique based on the HAM with Green's function for a class of nonlocal elliptic boundary value problems [Volume 9, Issue 3, 2021, Pages 722-735]
Convergence analysis An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions [Volume 9, Issue 4, 2021, Pages 1198-1213]
Convex function Bounds of Riemann-Liouville fractional integral operators [Volume 9, Issue 2, 2021, Pages 637-648]
Coupled Burgers’ equation An exponential cubic B-spline algorithm for solving the nonlinear Coupled Burgers’ equation [Volume 9, Issue 4, 2021, Pages 1109-1127]
Crank-Nicolson method Finite volume element approximation for time dependent convection diffusion reaction equations with memory [Volume 9, Issue 4, 2021, Pages 977-1000]
Critical exponents Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities [Volume 9, Issue 2, 2021, Pages 589-603]
Critical point theory Multiple solutions for a fourth-order elliptic equation involving singularity [Volume 9, Issue 3, 2021, Pages 818-829]
Cubic B-spline New exact solutions and numerical approximations of the generalized KdV equation [Volume 9, Issue 3, 2021, Pages 670-691]
Cusp bifurcations Global dynamics and numerical bifurcation of a bioeconomic system [Volume 9, Issue 2, 2021, Pages 427-445]

D

Daubechies wavelets ‎Solving brachistochrone problem via scaling functions of Daubechies wavelets [Volume 9, Issue 2, 2021, Pages 511-522]
Decoupled nonlinear Schr¨odinger’s equation On traveling wave solutions: the decoupled nonlinear Schrödinger equations with inter modal dispersion [Volume 9, Issue 1, 2021, Pages 52-62]
Delay differential equation VIM-Pad´e technique for solving nonlinear and delay initial value problems [Volume 9, Issue 3, 2021, Pages 749-761]
Delay term Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay [Volume 9, Issue 2, 2021, Pages 623-636]
Dependent Components Solving some stochastic differential equation using Dirichlet distributions [Volume 9, Issue 2, 2021, Pages 393-398]
Descriptor fractional discrete-time Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback [Volume 9, Issue 2, 2021, Pages 375-392]
Differential algebraic equations Analytical solution for descriptor system in partial differential equations [Volume 9, Issue 2, 2021, Pages 467-479]
Differential equations(DEs) Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Discrete mollification Regularization of a nonlinear inverse problem by discrete mollification‎ ‎method [Volume 9, Issue 1, 2021, Pages 313-326]
Discretization Numerical solution of fractional Riesz space telegraph equation [Volume 9, Issue 1, 2021, Pages 187-210]
Distributed order Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations [Volume 9, Issue 3, 2021, Pages 858-873]
Distributed-order fractional derivative Solving of partial differential equations with distributed order in time using fractional-order Bernoulli-Legendre functions [Volume 9, Issue 3, 2021, Pages 799-817]
Disturbance observer Sensitivity analytic and synchronization of a new fractional-order financial system [Volume 9, Issue 3, 2021, Pages 788-798]
Dynamical behavior Global dynamics and numerical bifurcation of a bioeconomic system [Volume 9, Issue 2, 2021, Pages 427-445]

E

Elliptic equation Application of the method of fundamental solutions for designing the optimal shape in heat transfer [Volume 9, Issue 1, 2021, Pages 273-288]
Ergodic Markov chain A new Monte Carlo method for solving systems of linear algebraic equations [Volume 9, Issue 1, 2021, Pages 159-179]
Error analysis ‎Solving brachistochrone problem via scaling functions of Daubechies wavelets [Volume 9, Issue 2, 2021, Pages 511-522]
Error analysis The numerical approximation for the solution of linear and nonlinear integral equations of the second kind by interpolating moving least squares [Volume 9, Issue 3, 2021, Pages 830-845]
Error estimation Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations [Volume 9, Issue 3, 2021, Pages 846-857]
Exact solutions The symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equation [Volume 9, Issue 4, 2021, Pages 1223-1232]
Existence and uniqueness Existence and uniqueness of solutions of uncertain linear systems [Volume 9, Issue 1, 2021, Pages 289-299]
Existence and uniqueness(EUS) Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Exponential cubic B-spline An exponential cubic B-spline algorithm for solving the nonlinear Coupled Burgers’ equation [Volume 9, Issue 4, 2021, Pages 1109-1127]
Extended trial equation method Exact solutions of the combined Hirota-LPD equation with variable coefficients [Volume 9, Issue 1, 2021, Pages 94-116]

F

Finance, Constant elasticity of variance A new methodology to estimate constant elasticity of variance [Volume 9, Issue 4, 2021, Pages 1059-1068]
Financing Meshless approach for pricing Islamic Ijarah under stochastic interest rate models [Volume 9, Issue 4, 2021, Pages 1028-1041]
Finite volume method Finite volume element approximation for time dependent convection diffusion reaction equations with memory [Volume 9, Issue 4, 2021, Pages 977-1000]
First order linear fuzzy differential equations First order linear fuzzy differential equations with fuzzy variable coefficients [Volume 9, Issue 1, 2021, Pages 1-21]
Fisher’s Equation Application of cubic B-spline collocation method for reaction diffusion Fisher's equation [Volume 9, Issue 1, 2021, Pages 22-35]
Flip bifurcation Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization [Volume 9, Issue 4, 2021, Pages 1013-1027]
Fokker-Planck equation Radial basis functions method for nonlinear time- and space-fractional Fokker-Planck equation [Volume 9, Issue 4, 2021, Pages 1128-1147]
Fokker-Plank equation Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process [Volume 9, Issue 1, 2021, Pages 258-272]
Forward-backward heat equation Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method [Volume 9, Issue 4, 2021, Pages 1083-1099]
Fractional BlackScholes equation A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]
Fractional cohomological equations Toward a new understanding of cohomological method for fractional partial differential equations [Volume 9, Issue 4, 2021, Pages 959-976]
Fractional derivative A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components [Volume 9, Issue 2, 2021, Pages 446-466]
Fractional derivative Radial basis functions method for nonlinear time- and space-fractional Fokker-Planck equation [Volume 9, Issue 4, 2021, Pages 1128-1147]
Fractional derivatives Solving a class of fractional optimal control problems via a new efficient and accurate method [Volume 9, Issue 2, 2021, Pages 480-492]
Fractional differential equations Stability and bifurcation of fractional tumor-immune model with time delay [Volume 9, Issue 3, 2021, Pages 692-709]
Fractional differential equations Collocation method based on Chebyshev polynomials for solving distributed order fractional differential equations [Volume 9, Issue 3, 2021, Pages 858-873]
Fractional differential equations On the existence and uniqueness of positive solutions for a p-Laplacian fractional boundary value problem with an integral boundary condition with a parameter [Volume 9, Issue 4, 2021, Pages 1001-1012]
Fractional differential equations(FDEs) Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Fractional equation Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations [Volume 9, Issue 3, 2021, Pages 762-773]
Fractional integral operator Solving of partial differential equations with distributed order in time using fractional-order Bernoulli-Legendre functions [Volume 9, Issue 3, 2021, Pages 799-817]
Fractional integrals Solving a class of fractional optimal control problems via a new efficient and accurate method [Volume 9, Issue 2, 2021, Pages 480-492]
Fractional optimal control problem Solving a class of fractional optimal control problems via a new efficient and accurate method [Volume 9, Issue 2, 2021, Pages 480-492]
Fractional-order dynamical system Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization [Volume 9, Issue 4, 2021, Pages 1013-1027]
Fractional order financial system Sensitivity analytic and synchronization of a new fractional-order financial system [Volume 9, Issue 3, 2021, Pages 788-798]
Fractional-order functions Solving of partial differential equations with distributed order in time using fractional-order Bernoulli-Legendre functions [Volume 9, Issue 3, 2021, Pages 799-817]
Fractional order Riccati differential equations Asymptotic decomposition method for fractional order Riccati differential equation [Volume 9, Issue 1, 2021, Pages 63-78]
Fractional Sturm-Liouville Eigenvalues of fractional Sturm-Liouville problems by successive method [Volume 9, Issue 4, 2021, Pages 1163-1175]
Fractional telegraph equation Numerical solution of fractional Riesz space telegraph equation [Volume 9, Issue 1, 2021, Pages 187-210]
Fredholm integral equation On the existence of positive solutions for a non-autonomous fractional differential equation with integral boundary conditions [Volume 9, Issue 1, 2021, Pages 36-51]
Fredholm integral equation Quintic Spline functions and Fredholm integral equation [Volume 9, Issue 1, 2021, Pages 211-224]
Fredholm integro-differential equation Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations [Volume 9, Issue 3, 2021, Pages 762-773]
Free boundary problem Solving free boundary problem for an initial cell layer in multispecies biofilm formation by Newton-Raphson method [Volume 9, Issue 3, 2021, Pages 899-907]
Free boundary problems A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems [Volume 9, Issue 2, 2021, Pages 410-426]
Full discrete scheme Finite volume element approximation for time dependent convection diffusion reaction equations with memory [Volume 9, Issue 4, 2021, Pages 977-1000]
Fuzzy blood flow back Theorem Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Fuzzy initial value problem First order linear fuzzy differential equations with fuzzy variable coefficients [Volume 9, Issue 1, 2021, Pages 1-21]
Fuzzy instant pressure volume Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Fuzzy integral equations Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations [Volume 9, Issue 3, 2021, Pages 846-857]
Fuzzy model of arterial pressure Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Fuzzy output blood ow theorem Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Fuzzy variable coefficients First order linear fuzzy differential equations with fuzzy variable coefficients [Volume 9, Issue 1, 2021, Pages 1-21]

G

Galerkin New exact solutions and numerical approximations of the generalized KdV equation [Volume 9, Issue 3, 2021, Pages 670-691]
Generalized Hukuhara difference Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Generalized Hukuhara differentiable Analytical fuzzy solution of the ventricular pressure equation and prediction of the blood pressure [Volume 9, Issue 4, 2021, Pages 919-939]
Generalized Korteweg-de Vries equation New exact solutions and numerical approximations of the generalized KdV equation [Volume 9, Issue 3, 2021, Pages 670-691]
Generalized symmetries Generalized symmetries and conservation laws of (3+1)-dimensional variable coefficient Zakharov-Kuznetsov equation [Volume 9, Issue 1, 2021, Pages 300-312]
General relativity search algorithm A new methodology to estimate constant elasticity of variance [Volume 9, Issue 4, 2021, Pages 1059-1068]
Genocchi polynomials Solving fractional optimal control problems using Genocchi polynomials [Volume 9, Issue 1, 2021, Pages 79-93]
Geometric flow Hyperbolic Ricci-Bourguignon flow [Volume 9, Issue 2, 2021, Pages 399-409]
Green’s function Inverse Sturm-Liouville problems with two supplementary discontinuous conditions on two symmetric disjoint intervals [Volume 9, Issue 1, 2021, Pages 244-257]

H

Hamiltonian boundary value problem An efficient numerical solution for time switching optimal control problems [Volume 9, Issue 1, 2021, Pages 225-243]
Hammerstein On the numerical treatment and analysis of Hammerstein integral equation [Volume 9, Issue 2, 2021, Pages 493-510]
Higher-order elliptic equations Multiple solutions for a fourth-order elliptic equation involving singularity [Volume 9, Issue 3, 2021, Pages 818-829]
HIV-1 model Optimal control of double delayed HIV-1 infection model of fighting a virus with another virus [Volume 9, Issue 3, 2021, Pages 874-885]
HIV infection Analysis of time delay model for drug therapy on HIV dynamics [Volume 9, Issue 2, 2021, Pages 577-588]
Homotopic approach An efficient numerical solution for time switching optimal control problems [Volume 9, Issue 1, 2021, Pages 225-243]
Hopf Bifurcation Global dynamics and numerical bifurcation of a bioeconomic system [Volume 9, Issue 2, 2021, Pages 427-445]
Hopf Bifurcation Stability and bifurcation of fractional tumor-immune model with time delay [Volume 9, Issue 3, 2021, Pages 692-709]
Hopf Bifurcation Analysis of time delay model for drug therapy on HIV dynamics [Volume 9, Issue 2, 2021, Pages 577-588]
Hybrid function Numerical analysis of fractional differential equation by TSI-wavelet method [Volume 9, Issue 3, 2021, Pages 659-669]
Hyers-Ulams(UH) stability Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Hyperbolic equation Hyperbolic Ricci-Bourguignon flow [Volume 9, Issue 2, 2021, Pages 399-409]

I

Image Denoising PDE-based hyperbolic-parabolic model for image denoising with forward-backward diffusivity [Volume 9, Issue 4, 2021, Pages 1100-1108]
Improved tan(ϕ/2)-expansion method Exact solutions of the combined Hirota-LPD equation with variable coefficients [Volume 9, Issue 1, 2021, Pages 94-116]
Infinite delay Stability in distribution of neutral stochastic functional differential equations with infinite delay [Volume 9, Issue 2, 2021, Pages 604-622]
Integral Boundary Condition On the existence and uniqueness of positive solutions for a p-Laplacian fractional boundary value problem with an integral boundary condition with a parameter [Volume 9, Issue 4, 2021, Pages 1001-1012]
Integral boundary conditions On the existence of positive solutions for a non-autonomous fractional differential equation with integral boundary conditions [Volume 9, Issue 1, 2021, Pages 36-51]
Integral equations An efficient technique based on the HAM with Green's function for a class of nonlocal elliptic boundary value problems [Volume 9, Issue 3, 2021, Pages 722-735]
Integration schemes On traveling wave solutions: the decoupled nonlinear Schrödinger equations with inter modal dispersion [Volume 9, Issue 1, 2021, Pages 52-62]
Intracellular delay Optimal control of double delayed HIV-1 infection model of fighting a virus with another virus [Volume 9, Issue 3, 2021, Pages 874-885]
Inverse Sturm-Liouville problems Inverse Sturm-Liouville problems with two supplementary discontinuous conditions on two symmetric disjoint intervals [Volume 9, Issue 1, 2021, Pages 244-257]
Iterative methods Constructing an efficient multi-step iterative scheme for nonlinear system of equations [Volume 9, Issue 3, 2021, Pages 710-721]
Iterative methods Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions [Volume 9, Issue 3, 2021, Pages 649-658]
Iterative system An infinite number of nonnegative solutions for iterative system of singular fractional order Boundary value problems [Volume 9, Issue 4, 2021, Pages 940-958]

K

Kirchhoff type problems Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities [Volume 9, Issue 2, 2021, Pages 589-603]

L

L1 scheme Non-uniform L1/DG method for one-dimensional time-fractional convection equation [Volume 9, Issue 4, 2021, Pages 1069-1082]
Lagrange multipliers method Solving a class of fractional optimal control problems via a new efficient and accurate method [Volume 9, Issue 2, 2021, Pages 480-492]
Laguerre collocation method A Laguerre approach for solving of the systems of linear differential equations and residual improvement [Volume 9, Issue 2, 2021, Pages 553-576]
Laguerre polynomials A Laguerre approach for solving of the systems of linear differential equations and residual improvement [Volume 9, Issue 2, 2021, Pages 553-576]
Lane-Emden type equations Laguerre collocation method for solving Lane-Emden type equations [Volume 9, Issue 4, 2021, Pages 1176-1197]
Laplace transform Conformable double Laplace transform method for solving conformable fractional partial differential equations [Volume 9, Issue 3, 2021, Pages 908-918]
Laplacian operator Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Legendre wavelets Solving a class of fractional optimal control problems via a new efficient and accurate method [Volume 9, Issue 2, 2021, Pages 480-492]
Lie point symmetry Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process [Volume 9, Issue 1, 2021, Pages 258-272]
Lifetime Solving some stochastic differential equation using Dirichlet distributions [Volume 9, Issue 2, 2021, Pages 393-398]
Likelihood function A new methodology to estimate constant elasticity of variance [Volume 9, Issue 4, 2021, Pages 1059-1068]
Local existence Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay [Volume 9, Issue 2, 2021, Pages 623-636]
Local fractional calculus An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients [Volume 9, Issue 3, 2021, Pages 774-787]
Logarithmic nonlinearity Local existence and blow up of solutions for a logarithmic nonlinear viscoelastic wave equation with delay [Volume 9, Issue 2, 2021, Pages 623-636]
Lyapunov stability Sensitivity analytic and synchronization of a new fractional-order financial system [Volume 9, Issue 3, 2021, Pages 788-798]

M

Mathematical Modeling A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth [Volume 9, Issue 2, 2021, Pages 327-346]
Meshless methods Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method [Volume 9, Issue 4, 2021, Pages 1083-1099]
Method of fundamental solutions Application of the method of fundamental solutions for designing the optimal shape in heat transfer [Volume 9, Issue 1, 2021, Pages 273-288]
Modified generalized Laguerre polynomials Laguerre collocation method for solving Lane-Emden type equations [Volume 9, Issue 4, 2021, Pages 1176-1197]
Monte Carlo method A new Monte Carlo method for solving systems of linear algebraic equations [Volume 9, Issue 1, 2021, Pages 159-179]
Mountain pass theorem Existence of solutions for a class of critical Kirchhoff type problems involving Caffarelli-Kohn-Nirenberg inequalities [Volume 9, Issue 2, 2021, Pages 589-603]
Moving least-squares method The numerical approximation for the solution of linear and nonlinear integral equations of the second kind by interpolating moving least squares [Volume 9, Issue 3, 2021, Pages 830-845]
Multigrid technique Semi-Algebraic mode analysis for finite element discretisations of the heat equation [Volume 9, Issue 1, 2021, Pages 146-158]
Multiquadric radial basis functions A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems [Volume 9, Issue 2, 2021, Pages 410-426]
M¨untz-Legendre polynomial Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process [Volume 9, Issue 1, 2021, Pages 258-272]

N

Neimark-Sacker bifurcation Dynamical behaviors of Bazykin-Berezovskaya model with fractional-order and its discretization [Volume 9, Issue 4, 2021, Pages 1013-1027]
Nelder-Mead algorithm A new methodology to estimate constant elasticity of variance [Volume 9, Issue 4, 2021, Pages 1059-1068]
Neutral stochastic functional differential equations Stability in distribution of neutral stochastic functional differential equations with infinite delay [Volume 9, Issue 2, 2021, Pages 604-622]
Newton method Radial basis functions method for nonlinear time- and space-fractional Fokker-Planck equation [Volume 9, Issue 4, 2021, Pages 1128-1147]
Newton-Raphson method Solving free boundary problem for an initial cell layer in multispecies biofilm formation by Newton-Raphson method [Volume 9, Issue 3, 2021, Pages 899-907]
Nonautonomous rogue wave Exact solutions of the combined Hirota-LPD equation with variable coefficients [Volume 9, Issue 1, 2021, Pages 94-116]
Nonlinear equations Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback [Volume 9, Issue 2, 2021, Pages 375-392]
Nonlinear initial value problem VIM-Pad´e technique for solving nonlinear and delay initial value problems [Volume 9, Issue 3, 2021, Pages 749-761]
Nonlinear inverse problem Regularization of a nonlinear inverse problem by discrete mollification‎ ‎method [Volume 9, Issue 1, 2021, Pages 313-326]
Nonlinear local fractional wave-like equations An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients [Volume 9, Issue 3, 2021, Pages 774-787]
Nonlinear nonlocal elliptic BVPs An efficient technique based on the HAM with Green's function for a class of nonlocal elliptic boundary value problems [Volume 9, Issue 3, 2021, Pages 722-735]
Nonlocal conditions Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions [Volume 9, Issue 3, 2021, Pages 649-658]
Non-overlapping domain decomposition Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method [Volume 9, Issue 4, 2021, Pages 1083-1099]
Nonsmooth optimization Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints [Volume 9, Issue 2, 2021, Pages 347-357]
Numerical analysis Laguerre collocation method for solving Lane-Emden type equations [Volume 9, Issue 4, 2021, Pages 1176-1197]
Numerical method Solving of partial differential equations with distributed order in time using fractional-order Bernoulli-Legendre functions [Volume 9, Issue 3, 2021, Pages 799-817]

O

One-dimensional hyperbolic telegraph equation An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions [Volume 9, Issue 4, 2021, Pages 1198-1213]
One phase obstacle problem A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems [Volume 9, Issue 2, 2021, Pages 410-426]
Operational matrices Numerical analysis of fractional differential equation by TSI-wavelet method [Volume 9, Issue 3, 2021, Pages 659-669]
Operational matrices Laguerre collocation method for solving Lane-Emden type equations [Volume 9, Issue 4, 2021, Pages 1176-1197]
Operational matrix Solving fractional optimal control problems using Genocchi polynomials [Volume 9, Issue 1, 2021, Pages 79-93]
Operational‎ ‎matrix Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations [Volume 9, Issue 3, 2021, Pages 762-773]
Optimal control A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]
Optimal control Optimal control of double delayed HIV-1 infection model of fighting a virus with another virus [Volume 9, Issue 3, 2021, Pages 874-885]
Optimal control problem A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components [Volume 9, Issue 2, 2021, Pages 446-466]
Optimal Control Problems Solving fractional optimal control problems using Genocchi polynomials [Volume 9, Issue 1, 2021, Pages 79-93]
Optimal homotopy analysis method An efficient technique based on the HAM with Green's function for a class of nonlocal elliptic boundary value problems [Volume 9, Issue 3, 2021, Pages 722-735]
Optimal shape Application of the method of fundamental solutions for designing the optimal shape in heat transfer [Volume 9, Issue 1, 2021, Pages 273-288]
Option pricing A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]

P

Padé technique VIM-Pad´e technique for solving nonlinear and delay initial value problems [Volume 9, Issue 3, 2021, Pages 749-761]
Parametric form of a Fuzzy number Bernoulli wavelet method for numerical solutions of system of fuzzy integral equations [Volume 9, Issue 3, 2021, Pages 846-857]
Parametric state feedback Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback [Volume 9, Issue 2, 2021, Pages 375-392]
Partial differential equation (PDE) Conformable double Laplace transform method for solving conformable fractional partial differential equations [Volume 9, Issue 3, 2021, Pages 908-918]
Partial eigenvalue assignment Partial eigenvalue assignment of descriptor fractional discrete-time linear systems by parametric state feedback [Volume 9, Issue 2, 2021, Pages 375-392]
Particle swarm algorithm A new methodology to estimate constant elasticity of variance [Volume 9, Issue 4, 2021, Pages 1059-1068]
P-Laplacian operator On the existence and uniqueness of positive solutions for a p-Laplacian fractional boundary value problem with an integral boundary condition with a parameter [Volume 9, Issue 4, 2021, Pages 1001-1012]
Polynomial approximation Numerical solution of fractional Riesz space telegraph equation [Volume 9, Issue 1, 2021, Pages 187-210]
Pontryagin Maximum Principle Optimal control of double delayed HIV-1 infection model of fighting a virus with another virus [Volume 9, Issue 3, 2021, Pages 874-885]
Product integration Asymptotic decomposition method for fractional order Riccati differential equation [Volume 9, Issue 1, 2021, Pages 63-78]

Q

Quadratic B-spline An approximation to the solution of one-dimensional hyperbolic telegraph equation based on the collocation of quadratic B-spline functions [Volume 9, Issue 4, 2021, Pages 1198-1213]
Quadrature On the numerical treatment and analysis of Hammerstein integral equation [Volume 9, Issue 2, 2021, Pages 493-510]
Quasi-interpolant On the numerical treatment and analysis of Hammerstein integral equation [Volume 9, Issue 2, 2021, Pages 493-510]

R

Radial basis function, Finite difference method Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system [Volume 9, Issue 2, 2021, Pages 358-374]
Radial basis functions Application of the method of fundamental solutions for designing the optimal shape in heat transfer [Volume 9, Issue 1, 2021, Pages 273-288]
Radial basis functions Solving the forward-backward heat equation with a non-overlapping domain decomposition method based on multiquadric RBF meshfree method [Volume 9, Issue 4, 2021, Pages 1083-1099]
Radial basis functions Radial basis functions method for nonlinear time- and space-fractional Fokker-Planck equation [Volume 9, Issue 4, 2021, Pages 1128-1147]
Rayleigh Approximate distributed controllability of nonlocal Rayleigh beam [Volume 9, Issue 1, 2021, Pages 180-186]
RBF method Meshless approach for pricing Islamic Ijarah under stochastic interest rate models [Volume 9, Issue 4, 2021, Pages 1028-1041]
Reaction-diffusion Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems [Volume 9, Issue 3, 2021, Pages 886-898]
Recombinant virus Optimal control of double delayed HIV-1 infection model of fighting a virus with another virus [Volume 9, Issue 3, 2021, Pages 874-885]
Reproducing kernel method Mixed reproducing kernel-based iterative approach for nonlinear boundary value problems with nonlocal conditions [Volume 9, Issue 3, 2021, Pages 649-658]
Riba Meshless approach for pricing Islamic Ijarah under stochastic interest rate models [Volume 9, Issue 4, 2021, Pages 1028-1041]
Riemann Liouville derivative Exact solutions and numerical simulations of time-fractional Fokker-Plank equation for special stochastic process [Volume 9, Issue 1, 2021, Pages 258-272]
Riemann-Liouville fractional derivative Numerical solution of fractional Riesz space telegraph equation [Volume 9, Issue 1, 2021, Pages 187-210]
Riemann-Liouville fractional integral operators Bounds of Riemann-Liouville fractional integral operators [Volume 9, Issue 2, 2021, Pages 637-648]
Riemann-Stieltjes integral An infinite number of nonnegative solutions for iterative system of singular fractional order Boundary value problems [Volume 9, Issue 4, 2021, Pages 940-958]
Riesz fractional equation Numerical solution of fractional Riesz space telegraph equation [Volume 9, Issue 1, 2021, Pages 187-210]

S

Schauder fixed point Existence and stability criterion for the results of fractional order Φp-Laplacian operator boundary value problem [Volume 9, Issue 4, 2021, Pages 1042-1058]
Segregation A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems [Volume 9, Issue 2, 2021, Pages 410-426]
Semi-Algebraic Mode Analysis Semi-Algebraic mode analysis for finite element discretisations of the heat equation [Volume 9, Issue 1, 2021, Pages 146-158]
Sensitivity analysis A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]
Showalter-type conditions Analytical solution for descriptor system in partial differential equations [Volume 9, Issue 2, 2021, Pages 467-479]
Singular integrals Asymptotic decomposition method for fractional order Riccati differential equation [Volume 9, Issue 1, 2021, Pages 63-78]
Singularly perturbed parabolic problems Accelerated fitted operator finite difference method for singularly perturbed parabolic reaction-diffusion problems [Volume 9, Issue 3, 2021, Pages 886-898]
Singular nonlinear boundary value problems Multiple solutions for a fourth-order elliptic equation involving singularity [Volume 9, Issue 3, 2021, Pages 818-829]
Soliton New exact solutions and numerical approximations of the generalized KdV equation [Volume 9, Issue 3, 2021, Pages 670-691]
Solution map Stability in distribution of neutral stochastic functional differential equations with infinite delay [Volume 9, Issue 2, 2021, Pages 604-622]
Solvable and unsolvable fractional differential equations Toward a new understanding of cohomological method for fractional partial differential equations [Volume 9, Issue 4, 2021, Pages 959-976]
Space marching Regularization of a nonlinear inverse problem by discrete mollification‎ ‎method [Volume 9, Issue 1, 2021, Pages 313-326]
Space-time-fractional heat equation Toward a new understanding of cohomological method for fractional partial differential equations [Volume 9, Issue 4, 2021, Pages 959-976]
Spectral meshless radial point interpolation (SMRPI) method Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system [Volume 9, Issue 2, 2021, Pages 358-374]
Spectral radius A new Monte Carlo method for solving systems of linear algebraic equations [Volume 9, Issue 1, 2021, Pages 159-179]
Spectral Ritz method A new numerical Bernoulli polynomial method for solving fractional optimal control problems with vector components [Volume 9, Issue 2, 2021, Pages 446-466]
SPline On the numerical treatment and analysis of Hammerstein integral equation [Volume 9, Issue 2, 2021, Pages 493-510]
Stability Regularization of a nonlinear inverse problem by discrete mollification‎ ‎method [Volume 9, Issue 1, 2021, Pages 313-326]
Stability Analysis of time delay model for drug therapy on HIV dynamics [Volume 9, Issue 2, 2021, Pages 577-588]
Stability analysis A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]
Stability analysis Stability and bifurcation of fractional tumor-immune model with time delay [Volume 9, Issue 3, 2021, Pages 692-709]
Stability analysis An exponential cubic B-spline algorithm for solving the nonlinear Coupled Burgers’ equation [Volume 9, Issue 4, 2021, Pages 1109-1127]
Stability in distribution Stability in distribution of neutral stochastic functional differential equations with infinite delay [Volume 9, Issue 2, 2021, Pages 604-622]
Stationary conditions Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints [Volume 9, Issue 2, 2021, Pages 347-357]
Stochastic differential equations Meshless approach for pricing Islamic Ijarah under stochastic interest rate models [Volume 9, Issue 4, 2021, Pages 1028-1041]
Stochastic Linear Combination Solving some stochastic differential equation using Dirichlet distributions [Volume 9, Issue 2, 2021, Pages 393-398]
Strictly hyperbolicity Hyperbolic Ricci-Bourguignon flow [Volume 9, Issue 2, 2021, Pages 399-409]
Sucssesive methods Eigenvalues of fractional Sturm-Liouville problems by successive method [Volume 9, Issue 4, 2021, Pages 1163-1175]
Sukuk Meshless approach for pricing Islamic Ijarah under stochastic interest rate models [Volume 9, Issue 4, 2021, Pages 1028-1041]
Sumudu variational iteration method An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients [Volume 9, Issue 3, 2021, Pages 774-787]
Switching controls An efficient numerical solution for time switching optimal control problems [Volume 9, Issue 1, 2021, Pages 225-243]
System of linear algebraic equations A new Monte Carlo method for solving systems of linear algebraic equations [Volume 9, Issue 1, 2021, Pages 159-179]
Systems of linear differential equations A Laguerre approach for solving of the systems of linear differential equations and residual improvement [Volume 9, Issue 2, 2021, Pages 553-576]

T

The cross product of fuzzy numbers First order linear fuzzy differential equations with fuzzy variable coefficients [Volume 9, Issue 1, 2021, Pages 1-21]
Tikhonov regularization Application of the method of fundamental solutions for designing the optimal shape in heat transfer [Volume 9, Issue 1, 2021, Pages 273-288]
Time-dependent parameters A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [Volume 9, Issue 2, 2021, Pages 523-552]
Time scale Second order boundary value problems of nonsingular type on time scales [Volume 9, Issue 4, 2021, Pages 1214-1222]
Transition probability matrix A new Monte Carlo method for solving systems of linear algebraic equations [Volume 9, Issue 1, 2021, Pages 159-179]
Tumor Growth A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth [Volume 9, Issue 2, 2021, Pages 327-346]
Turing systems Numerical investigation based on a local meshless radial point interpolation for solving coupled nonlinear reaction-diffusion system [Volume 9, Issue 2, 2021, Pages 358-374]
Two-phase membrane A combining method for the approximate solution of spatial segregation limit of reaction-diffusion systems [Volume 9, Issue 2, 2021, Pages 410-426]
Two stage iterative method Numerical analysis of fractional differential equation by TSI-wavelet method [Volume 9, Issue 3, 2021, Pages 659-669]

U

Uncertain differential equations Existence and uniqueness of solutions of uncertain linear systems [Volume 9, Issue 1, 2021, Pages 289-299]

V

Vanishing constraints Necessary and sufficient conditions for M-stationarity of nonsmooth optimization problems with vanishing constraints [Volume 9, Issue 2, 2021, Pages 347-357]
Variational methods Multiple solutions for a fourth-order elliptic equation involving singularity [Volume 9, Issue 3, 2021, Pages 818-829]
Vc-ZK equation Generalized symmetries and conservation laws of (3+1)-dimensional variable coefficient Zakharov-Kuznetsov equation [Volume 9, Issue 1, 2021, Pages 300-312]
VIM-Pade technique VIM-Pad´e technique for solving nonlinear and delay initial value problems [Volume 9, Issue 3, 2021, Pages 749-761]
Volterra-Fredholm integro-differential equations The numerical approximation for the solution of linear and nonlinear integral equations of the second kind by interpolating moving least squares [Volume 9, Issue 3, 2021, Pages 830-845]

W

Waveform relaxation method Semi-Algebraic mode analysis for finite element discretisations of the heat equation [Volume 9, Issue 1, 2021, Pages 146-158]
Waveform relaxation method Extending a new two-grid waveform relaxation on a spatial finite element discretization [Volume 9, Issue 4, 2021, Pages 1148-1162]
Weyl m-function Inverse Sturm-Liouville problems with two supplementary discontinuous conditions on two symmetric disjoint intervals [Volume 9, Issue 1, 2021, Pages 244-257]

Z

Zika Virus A mathematical analysis of Zika virus transmission with optimal control strategies [Volume 9, Issue 1, 2021, Pages 117-145]