Computational Methods for Differential Equations

Keyword Index

A

Adaptive methods A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic [Volume 10, Issue 4, 2022, Pages 1007-1026]
Adaptive Monte Carlo algorithm An adaptive Monte Carlo algorithm for European and American options [Volume 10, Issue 2, 2022, Pages 489-501]
Adjoints A novel local meshless scheme based on the radial basis function for pricing multi-asset options [Volume 10, Issue 3, 2022, Pages 716-725]
Ansatz method Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods [Volume 10, Issue 3, 2022, Pages 674-685]

B

Backward bifurcation Backward bifurcation in a two strain model of heroin addiction [Volume 10, Issue 3, 2022, Pages 656-673]
Backward bifurcation An epidemic model for drug addiction [Volume 10, Issue 4, 2022, Pages 876-893]
Basin of attraction A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic [Volume 10, Issue 4, 2022, Pages 1007-1026]
Bellman’s optimality principle A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation [Volume 10, Issue 4, 2022, Pages 894-904]
Bernoulli functions A numerical scheme for solving time-fractional Bessel differential equations [Volume 10, Issue 4, 2022, Pages 1097-1114]
Bernoulli Tau method A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation [Volume 10, Issue 4, 2022, Pages 894-904]
Beta-fractional derivative Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative [Volume 10, Issue 2, 2022, Pages 549-566]
Black Scholes formulas PDTM approach to solve Black Scholes equation for powered ML-Payoff function [Volume 10, Issue 2, 2022, Pages 320-326]
Black Scholes model An adaptive Monte Carlo algorithm for European and American options [Volume 10, Issue 2, 2022, Pages 489-501]
Black-Scholes models Exact solutions and numerical simulation for Bakstein-Howison model [Volume 10, Issue 2, 2022, Pages 461-474]
Boundary value problems Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique [Volume 10, Issue 4, 2022, Pages 986-1006]
Brownian Motion A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process [Volume 10, Issue 1, 2022, Pages 61-76]
B-spline collocation Parameter-uniform robust scheme for singularly perturbed parabolic convection-diffusion problems with large time-lag [Volume 10, Issue 4, 2022, Pages 954-968]
Burgers equation Obtaining soliton solutions of equations combined with the Burgers and equal width wave equations using a novel method [Volume 10, Issue 3, 2022, Pages 826-836]

C

Caputo and Rieman-Liouville fractional derivative and integral A numerical scheme for solving time-fractional Bessel differential equations [Volume 10, Issue 4, 2022, Pages 1097-1114]
Caputo derivative Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials [Volume 10, Issue 2, 2022, Pages 431-444]
Caputo derivative Numerical solution for solving fractional parabolic partial differential equations [Volume 10, Issue 1, 2022, Pages 121-143]
Caputo derivative Analysis of non-hyperbolic equilibria for Caputo fractional system [Volume 10, Issue 2, 2022, Pages 298-306]
Caputo derivative A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials [Volume 10, Issue 3, 2022, Pages 755-773]
Caputo-Fabrizio fractional derivative A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability [Volume 10, Issue 1, 2022, Pages 12-27]
Caputo fractional derivative Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative [Volume 10, Issue 1, 2022, Pages 200-214]
Caputo’s derivative A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process [Volume 10, Issue 1, 2022, Pages 61-76]
Caratheodory map Existence of solution for nonlinear integral inclusions [Volume 10, Issue 1, 2022, Pages 215-224]
Cauchy-type problem Qualitative analysis of fractional differential equations with ψ-Hilfer fractional derivative [Volume 10, Issue 1, 2022, Pages 1-11]
Center manifold Analysis of non-hyperbolic equilibria for Caputo fractional system [Volume 10, Issue 2, 2022, Pages 298-306]
Chaos theory An interval chaos insight to iterative decomposition method for Rossler differential equation by considering stable uncertain coefficients [Volume 10, Issue 4, 2022, Pages 1115-1122]
Chaotic systems Optimal control of satellite attitude and its stability based on quaternion parameters [Volume 10, Issue 1, 2022, Pages 168-178]
Chaotic systems An interval chaos insight to iterative decomposition method for Rossler differential equation by considering stable uncertain coefficients [Volume 10, Issue 4, 2022, Pages 1115-1122]
Chebyshev polynomials An efficient approximate solution of Riesz fractional advection-diffusion equation [Volume 10, Issue 2, 2022, Pages 307-319]
Chebyshev spectral collocation method Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs [Volume 10, Issue 4, 2022, Pages 914-927]
Clique polynomial A study on homotopy analysis method and clique polynomial method [Volume 10, Issue 3, 2022, Pages 774-788]
Collocation method Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation [Volume 10, Issue 1, 2022, Pages 28-43]
Collocation method Studying the thermal analysis of rectangular cross section porous fin: A numerical approach [Volume 10, Issue 2, 2022, Pages 338-350]
Collocation method Shifted Jacobi collocation method for Volterra-Fredholm integral equation [Volume 10, Issue 2, 2022, Pages 408-418]
Collocation method Approximate price of the option under discretization by applying fractional quadratic interpolation [Volume 10, Issue 4, 2022, Pages 1075-1085]
Collocation method A novel perspective for simulations of the MEW equation by trigonometric cubic B-spline collocation method based on Rubin-Graves type linearization [Volume 10, Issue 4, 2022, Pages 1046-1058]
Common fixed point problem Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems [Volume 10, Issue 3, 2022, Pages 639-655]
Complete graph A study on homotopy analysis method and clique polynomial method [Volume 10, Issue 3, 2022, Pages 774-788]
Conformable derivative An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity [Volume 10, Issue 3, 2022, Pages 701-715]
Conformable derivative The generalized conformable derivative for 4α-order Sturm-Liouville problems [Volume 10, Issue 3, 2022, Pages 816-825]
Conformable fractional differential equations New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform [Volume 10, Issue 2, 2022, Pages 396-407]
Conservation laws Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation [Volume 10, Issue 3, 2022, Pages 608-616]
Continuous dependence Qualitative analysis of fractional differential equations with ψ-Hilfer fractional derivative [Volume 10, Issue 1, 2022, Pages 1-11]
Controllability Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative [Volume 10, Issue 1, 2022, Pages 200-214]
Convergence Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations [Volume 10, Issue 3, 2022, Pages 617-638]
Convergence analysis Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems [Volume 10, Issue 4, 2022, Pages 942-953]
Convergence analysis A numerical scheme for solving time-fractional Bessel differential equations [Volume 10, Issue 4, 2022, Pages 1097-1114]
Convex function New midpoint type inequalities for generalized fractional integral [Volume 10, Issue 1, 2022, Pages 93-108]
Coupled Burgers’ equation An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]
Coupled higher-order numerical model Application of variation of parameter’s method for hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates [Volume 10, Issue 3, 2022, Pages 580-594]
Covid-19 A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes [Volume 10, Issue 3, 2022, Pages 738-745]
Crank-Nicolson method Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation [Volume 10, Issue 1, 2022, Pages 28-43]
Crank-Nicolson scheme An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]
Cross viscosity Study of the non-Newtonian behaviour of Reiner Rivlin relative to power law in arterial stenosis [Volume 10, Issue 4, 2022, Pages 928-941]
Cubic B-spline Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation [Volume 10, Issue 1, 2022, Pages 28-43]
Cubic B-splines An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]

D

Delay parabolic differential equation A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability [Volume 10, Issue 2, 2022, Pages 475-488]
Delay Systems Sliding mode control of a class of uncertain nonlinear fractional-order time-varying delayed systems based on Razumikhin approach [Volume 10, Issue 4, 2022, Pages 860-875]
Differential games A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation [Volume 10, Issue 4, 2022, Pages 894-904]
Differential quadrature method A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions [Volume 10, Issue 4, 2022, Pages 969-985]
Differential quadrature method Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy [Volume 10, Issue 4, 2022, Pages 837-859]
Diffusion equation Exact solutions of diffusion equation on sphere [Volume 10, Issue 3, 2022, Pages 789-798]
Discretization matrix Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy [Volume 10, Issue 4, 2022, Pages 837-859]
Domain Decomposition Method An anomalous diffusion approach for speckle noise reduction in medical ultrasound images [Volume 10, Issue 1, 2022, Pages 225-235]
Drazin inverse Controllability and observability of linear impulsive differential algebraic system with Caputo fractional derivative [Volume 10, Issue 1, 2022, Pages 200-214]
Drinfel’d–Sokolov system Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method [Volume 10, Issue 4, 2022, Pages 1086-1096]
Drug addiction An epidemic model for drug addiction [Volume 10, Issue 4, 2022, Pages 876-893]

E

Economic growth model Numerical solution of optimal control problem for economic growth model using RBF collocation method [Volume 10, Issue 2, 2022, Pages 327-337]
Epidemic model Backward bifurcation in a two strain model of heroin addiction [Volume 10, Issue 3, 2022, Pages 656-673]
Epidemic model An epidemic model for drug addiction [Volume 10, Issue 4, 2022, Pages 876-893]
Equilibrium problem Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems [Volume 10, Issue 3, 2022, Pages 639-655]
Error analysis A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability [Volume 10, Issue 1, 2022, Pages 12-27]
Error analysis Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems [Volume 10, Issue 4, 2022, Pages 942-953]
Error analysis Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs [Volume 10, Issue 4, 2022, Pages 914-927]
European and American put option An adaptive Monte Carlo algorithm for European and American options [Volume 10, Issue 2, 2022, Pages 489-501]
Exact analytical solutions New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform [Volume 10, Issue 2, 2022, Pages 396-407]
Exact solutions Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods [Volume 10, Issue 3, 2022, Pages 674-685]
Exponential cubic spline method A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability [Volume 10, Issue 2, 2022, Pages 475-488]
Exponential Euler scheme The convergence of exponential Euler method for weighted fractional stochastic equations [Volume 10, Issue 2, 2022, Pages 538-548]
Exp(−Φ(ξ))-expansion method An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity [Volume 10, Issue 3, 2022, Pages 701-715]
Extended sinh-Gordon equation expansion method Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger’s equation [Volume 10, Issue 1, 2022, Pages 179-190]
Extragradient method Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems [Volume 10, Issue 3, 2022, Pages 639-655]

F

Feedback Nash equilibrium A Bernoulli Tau method for numerical solution of feedback Nash differential games with an error estimation [Volume 10, Issue 4, 2022, Pages 894-904]
Fifth-order integrable equations Some new soliton solutions for the nonlinear the fifth-order integrable equations [Volume 10, Issue 2, 2022, Pages 445-460]
Finite differences Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation [Volume 10, Issue 3, 2022, Pages 799-815]
Finite volume technique Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique [Volume 10, Issue 4, 2022, Pages 986-1006]
Floating point arithmetic Bounding error of calculating the matrix functions [Volume 10, Issue 1, 2022, Pages 259-273]
Fractal calculus Local fractal Fourier transform and applications [Volume 10, Issue 3, 2022, Pages 595-607]
Fractional cubic-quartic nonlinear Schr¨odinger equation An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity [Volume 10, Issue 3, 2022, Pages 701-715]
Fractional derivatives Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation [Volume 10, Issue 3, 2022, Pages 799-815]
Fractional difference equation Existence and properties of positive solutions for Caputo fractional difference equation and applications [Volume 10, Issue 3, 2022, Pages 567-579]
Fractional differential operator Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature [Volume 10, Issue 2, 2022, Pages 372-395]
Fractional diffusion equation Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials [Volume 10, Issue 2, 2022, Pages 431-444]
Fractional diffusion equation Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation [Volume 10, Issue 3, 2022, Pages 799-815]
Fractional equation Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation [Volume 10, Issue 3, 2022, Pages 608-616]
Fractional Laplace transform New analytical methods for solving a class of conformable fractional differential equations by fractional Laplace transform [Volume 10, Issue 2, 2022, Pages 396-407]
Fractional optimal control problem A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials [Volume 10, Issue 3, 2022, Pages 755-773]
Fractional-order differential equation A numerical scheme for solving time-fractional Bessel differential equations [Volume 10, Issue 4, 2022, Pages 1097-1114]
Fractional order systems Sliding mode control of a class of uncertain nonlinear fractional-order time-varying delayed systems based on Razumikhin approach [Volume 10, Issue 4, 2022, Pages 860-875]
Fractional Perona-Malik Equation An anomalous diffusion approach for speckle noise reduction in medical ultrasound images [Volume 10, Issue 1, 2022, Pages 225-235]
Fractional Sturm-Liouville The generalized conformable derivative for 4α-order Sturm-Liouville problems [Volume 10, Issue 3, 2022, Pages 816-825]
Fuzzy basis functions Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems [Volume 10, Issue 2, 2022, Pages 351-371]

G

Gegenbauer polynomial Numerical solution of space fractional diffusion equation using shifted Gegenbauer polynomials [Volume 10, Issue 2, 2022, Pages 431-444]
Generalized Burgers-Huxley equation Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines [Volume 10, Issue 3, 2022, Pages 686-700]
Geometric Brownian motion Stochastic analysis and invariant subspace method for handling option pricing with numerical simulation [Volume 10, Issue 2, 2022, Pages 419-430]
Global meshless method A meshless technique based on the radial basis functions for solving systems of partial differential equations [Volume 10, Issue 2, 2022, Pages 526-537]
Global stability Backward bifurcation in a two strain model of heroin addiction [Volume 10, Issue 3, 2022, Pages 656-673]
Global stability An epidemic model for drug addiction [Volume 10, Issue 4, 2022, Pages 876-893]
Green’s function Existence and properties of positive solutions for Caputo fractional difference equation and applications [Volume 10, Issue 3, 2022, Pages 567-579]

H

Haar wavelets method Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method [Volume 10, Issue 4, 2022, Pages 1086-1096]
Hammerstein integral equations On the numerical scheme for solving non-linear two-dimensional Hammerstein integral equations [Volume 10, Issue 4, 2022, Pages 1059-1074]
Hermite-Hadamard inequality New midpoint type inequalities for generalized fractional integral [Volume 10, Issue 1, 2022, Pages 93-108]
H¨older continuity Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems [Volume 10, Issue 3, 2022, Pages 639-655]
Hyers-Ulam stability Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays [Volume 10, Issue 1, 2022, Pages 191-199]
Hyperbolic telegraph equation Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy [Volume 10, Issue 4, 2022, Pages 837-859]

I

Images Denoising An anomalous diffusion approach for speckle noise reduction in medical ultrasound images [Volume 10, Issue 1, 2022, Pages 225-235]
Improved tanh(ϕ/2)-expansion method Some new soliton solutions for the nonlinear the fifth-order integrable equations [Volume 10, Issue 2, 2022, Pages 445-460]
Incompressible flow Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique [Volume 10, Issue 4, 2022, Pages 986-1006]
Initial value problem An interval version of the Kuntzmann-Butcher method for solving the initial value problem [Volume 10, Issue 1, 2022, Pages 44-60]
Integrodifferential equations Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays [Volume 10, Issue 1, 2022, Pages 191-199]
Interval arithmetic Bounding error of calculating the matrix functions [Volume 10, Issue 1, 2022, Pages 259-273]
Interval decomposition method An interval chaos insight to iterative decomposition method for Rossler differential equation by considering stable uncertain coefficients [Volume 10, Issue 4, 2022, Pages 1115-1122]
Iterative method On the numerical scheme for solving non-linear two-dimensional Hammerstein integral equations [Volume 10, Issue 4, 2022, Pages 1059-1074]
Itˆo-Taylor expansion Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations [Volume 10, Issue 3, 2022, Pages 617-638]

K

Krasnoselskii fixed point theorem Existence of solution for nonlinear integral inclusions [Volume 10, Issue 1, 2022, Pages 215-224]
Kronecker product Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs [Volume 10, Issue 4, 2022, Pages 914-927]
Kuntzmann-Butcher method An interval version of the Kuntzmann-Butcher method for solving the initial value problem [Volume 10, Issue 1, 2022, Pages 44-60]

L

Lagrange multipliers Numerical solution of optimal control problem for economic growth model using RBF collocation method [Volume 10, Issue 2, 2022, Pages 327-337]
Least square method A numerical scheme for solving time-fractional Bessel differential equations [Volume 10, Issue 4, 2022, Pages 1097-1114]
Legendre polynomials Approximate price of the option under discretization by applying fractional quadratic interpolation [Volume 10, Issue 4, 2022, Pages 1075-1085]
Lid-driven cavity Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique [Volume 10, Issue 4, 2022, Pages 986-1006]
Lie Subalgebras Exact solutions of diffusion equation on sphere [Volume 10, Issue 3, 2022, Pages 789-798]
Lie symmetries Exact solutions and numerical simulation for Bakstein-Howison model [Volume 10, Issue 2, 2022, Pages 461-474]
Lie symmetry analysis Lie symmetries, exact solutions, and conservation laws of the nonlinear time-fractional Benjamin-Ono equation [Volume 10, Issue 3, 2022, Pages 608-616]
Linear Partial differential equations Error analysis and Kronecker implementation of Chebyshev spectral collocation method for solving linear PDEs [Volume 10, Issue 4, 2022, Pages 914-927]
Localized Meshfree Method An anomalous diffusion approach for speckle noise reduction in medical ultrasound images [Volume 10, Issue 1, 2022, Pages 225-235]
Local radial basis function A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions [Volume 10, Issue 4, 2022, Pages 969-985]

M

Malliavin calculus The convergence of exponential Euler method for weighted fractional stochastic equations [Volume 10, Issue 2, 2022, Pages 538-548]
Markov chain Stochastic analysis and invariant subspace method for handling option pricing with numerical simulation [Volume 10, Issue 2, 2022, Pages 419-430]
Matrix function Bounding error of calculating the matrix functions [Volume 10, Issue 1, 2022, Pages 259-273]
Mean-square stability Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations [Volume 10, Issue 3, 2022, Pages 617-638]
Medical Ultrasound Images An anomalous diffusion approach for speckle noise reduction in medical ultrasound images [Volume 10, Issue 1, 2022, Pages 225-235]
Meshless method A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions [Volume 10, Issue 4, 2022, Pages 969-985]
Meta-heuristic Design of normal distribution-based algorithm for solving systems of nonlinear equations [Volume 10, Issue 1, 2022, Pages 274-297]
Method of lines A meshless technique based on the radial basis functions for solving systems of partial differential equations [Volume 10, Issue 2, 2022, Pages 526-537]
Method of lines Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines [Volume 10, Issue 3, 2022, Pages 686-700]
Mittag-Leffler function Regularized Prabhakar derivative for partial differential equations [Volume 10, Issue 3, 2022, Pages 726-737]
Mittag-Leffler functions The generalized conformable derivative for 4α-order Sturm-Liouville problems [Volume 10, Issue 3, 2022, Pages 816-825]
ML-Payoff functions PDTM approach to solve Black Scholes equation for powered ML-Payoff function [Volume 10, Issue 2, 2022, Pages 320-326]
Modified cubic B-spline basis functions Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy [Volume 10, Issue 4, 2022, Pages 837-859]
Modified equal width wave equation Obtaining soliton solutions of equations combined with the Burgers and equal width wave equations using a novel method [Volume 10, Issue 3, 2022, Pages 826-836]
Modified hat functions, Error estimate A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process [Volume 10, Issue 1, 2022, Pages 61-76]
Modified Jacobi elliptic functions Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis [Volume 10, Issue 4, 2022, Pages 905-913]
Modified Kudryashov method Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods [Volume 10, Issue 3, 2022, Pages 674-685]
Monotonicity The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8 [Volume 10, Issue 1, 2022, Pages 236-258]
Mott polynomials basis A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials [Volume 10, Issue 3, 2022, Pages 755-773]
Moving least square A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions [Volume 10, Issue 4, 2022, Pages 969-985]
Multiple strain Backward bifurcation in a two strain model of heroin addiction [Volume 10, Issue 3, 2022, Pages 656-673]
Multiquadric quasi-interpolation Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines [Volume 10, Issue 3, 2022, Pages 686-700]

N

Navier-Stokes equations Numerical analysis of fluid flow behaviour in two sided deep lid driven cavity using the finite volume technique [Volume 10, Issue 4, 2022, Pages 986-1006]
New powerful expansion approach Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative [Volume 10, Issue 2, 2022, Pages 549-566]
NLSE Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger’s equation [Volume 10, Issue 1, 2022, Pages 179-190]
NLSE Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis [Volume 10, Issue 4, 2022, Pages 905-913]
Nonlinear differential equation A study on homotopy analysis method and clique polynomial method [Volume 10, Issue 3, 2022, Pages 774-788]
Nonlinear equations Design of normal distribution-based algorithm for solving systems of nonlinear equations [Volume 10, Issue 1, 2022, Pages 274-297]
Nonlinear equations A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic [Volume 10, Issue 4, 2022, Pages 1007-1026]
Nonlinear integral inclusions Existence of solution for nonlinear integral inclusions [Volume 10, Issue 1, 2022, Pages 215-224]
Nonlinear parabolic partial differential equation Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation [Volume 10, Issue 1, 2022, Pages 28-43]
Nonlinear partial differential equations Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative [Volume 10, Issue 2, 2022, Pages 549-566]
Non-uniform mesh Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation [Volume 10, Issue 1, 2022, Pages 28-43]
Normal Distribution-based Algorithm (NDA) Design of normal distribution-based algorithm for solving systems of nonlinear equations [Volume 10, Issue 1, 2022, Pages 274-297]
Norm-bound perturbation Sliding mode control of a class of uncertain nonlinear fractional-order time-varying delayed systems based on Razumikhin approach [Volume 10, Issue 4, 2022, Pages 860-875]
Numerical Studying the thermal analysis of rectangular cross section porous fin: A numerical approach [Volume 10, Issue 2, 2022, Pages 338-350]
Numerical methods A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability [Volume 10, Issue 1, 2022, Pages 12-27]
Numerical optimization Design of normal distribution-based algorithm for solving systems of nonlinear equations [Volume 10, Issue 1, 2022, Pages 274-297]
Numerical simulation A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes [Volume 10, Issue 3, 2022, Pages 738-745]
Numerical solution Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method [Volume 10, Issue 4, 2022, Pages 1086-1096]

O

Oldroyd-B fluid Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature [Volume 10, Issue 2, 2022, Pages 372-395]
Operational matrices An efficient approximate solution of Riesz fractional advection-diffusion equation [Volume 10, Issue 2, 2022, Pages 307-319]
Operational matrix A numerical method for solving fractional optimal control problems using the operational matrix of Mott polynomials [Volume 10, Issue 3, 2022, Pages 755-773]
Optical soliton Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger’s equation [Volume 10, Issue 1, 2022, Pages 179-190]
Optical soliton Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis [Volume 10, Issue 4, 2022, Pages 905-913]
Optimal collocation method An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]
Optimal control Optimal control of satellite attitude and its stability based on quaternion parameters [Volume 10, Issue 1, 2022, Pages 168-178]
Optimal control problem Numerical solution of optimal control problem for economic growth model using RBF collocation method [Volume 10, Issue 2, 2022, Pages 327-337]
Optimal Control Problems Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems [Volume 10, Issue 2, 2022, Pages 351-371]
Optimality conditions Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems [Volume 10, Issue 2, 2022, Pages 351-371]
Option pricing Stochastic analysis and invariant subspace method for handling option pricing with numerical simulation [Volume 10, Issue 2, 2022, Pages 419-430]
Ornstein Uhlenbeck process A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes [Volume 10, Issue 3, 2022, Pages 738-745]
Oscillatory systems of fractional derivative Asymptotic method for solution of oscillatory fractional derivative [Volume 10, Issue 4, 2022, Pages 1123-1130]

P

Period function The monotonicity and convexity of the period function for a class of symmetric Newtonian systems of degree 8 [Volume 10, Issue 1, 2022, Pages 236-258]
Perturbation Study of the non-Newtonian behaviour of Reiner Rivlin relative to power law in arterial stenosis [Volume 10, Issue 4, 2022, Pages 928-941]
Porous Fin Studying the thermal analysis of rectangular cross section porous fin: A numerical approach [Volume 10, Issue 2, 2022, Pages 338-350]
Positive solution Existence and properties of positive solutions for Caputo fractional difference equation and applications [Volume 10, Issue 3, 2022, Pages 567-579]
Projected Differential Transform Method PDTM approach to solve Black Scholes equation for powered ML-Payoff function [Volume 10, Issue 2, 2022, Pages 320-326]
Pseudo-differential operators A novel local meshless scheme based on the radial basis function for pricing multi-asset options [Volume 10, Issue 3, 2022, Pages 716-725]

Q

Quadrature formula On the numerical scheme for solving non-linear two-dimensional Hammerstein integral equations [Volume 10, Issue 4, 2022, Pages 1059-1074]
Quasilinearization An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]
Quasilinearization technique Numerical solution of Drinfel’d–Sokolov system with the Haar wavelets method [Volume 10, Issue 4, 2022, Pages 1086-1096]

R

Radial basis function Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations [Volume 10, Issue 1, 2022, Pages 144-157]
Radial basis functions A meshless technique based on the radial basis functions for solving systems of partial differential equations [Volume 10, Issue 2, 2022, Pages 526-537]
Ramped velocity and temperature Fractional study on heat and mass transfer of MHD Oldroyd-B fluid with ramped velocity and temperature [Volume 10, Issue 2, 2022, Pages 372-395]
Random impulsive Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays [Volume 10, Issue 1, 2022, Pages 191-199]
RBF collocation method Numerical solution of optimal control problem for economic growth model using RBF collocation method [Volume 10, Issue 2, 2022, Pages 327-337]
Reduction equations Exact solutions of diffusion equation on sphere [Volume 10, Issue 3, 2022, Pages 789-798]
Regularized Prabhakar derivative Regularized Prabhakar derivative for partial differential equations [Volume 10, Issue 3, 2022, Pages 726-737]
Reiner-Rivlin Fluid Study of the non-Newtonian behaviour of Reiner Rivlin relative to power law in arterial stenosis [Volume 10, Issue 4, 2022, Pages 928-941]
Reproducing kernel method Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems [Volume 10, Issue 4, 2022, Pages 942-953]
Ricci soliton Exact solutions of diffusion equation on sphere [Volume 10, Issue 3, 2022, Pages 789-798]
Riesz fractional advection-diffusion An efficient approximate solution of Riesz fractional advection-diffusion equation [Volume 10, Issue 2, 2022, Pages 307-319]
Riesz fractional derivative Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation [Volume 10, Issue 3, 2022, Pages 799-815]
Rogue wave Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis [Volume 10, Issue 4, 2022, Pages 905-913]
R-order convergence A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic [Volume 10, Issue 4, 2022, Pages 1007-1026]
Rossler differential equations An interval chaos insight to iterative decomposition method for Rossler differential equation by considering stable uncertain coefficients [Volume 10, Issue 4, 2022, Pages 1115-1122]
Runge-Kutta methods An interval version of the Kuntzmann-Butcher method for solving the initial value problem [Volume 10, Issue 1, 2022, Pages 44-60]

S

Self accelerating parameter A two-step method adaptive with memory with eighth-order for solving nonlinear equations and its dynamic [Volume 10, Issue 4, 2022, Pages 1007-1026]
Semi-smooth Newton method Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems [Volume 10, Issue 2, 2022, Pages 351-371]
Separation-Preserving operators A novel local meshless scheme based on the radial basis function for pricing multi-asset options [Volume 10, Issue 3, 2022, Pages 716-725]
Shifted Legendre Tau method Numerical solution for solving fractional parabolic partial differential equations [Volume 10, Issue 1, 2022, Pages 121-143]
Shrinking projection Hybrid shrinking projection extragradient-like algorithms for equilibrium and fixed point problems [Volume 10, Issue 3, 2022, Pages 639-655]
Simple equation method Obtaining soliton solutions of equations combined with the Burgers and equal width wave equations using a novel method [Volume 10, Issue 3, 2022, Pages 826-836]
Singularly perturbed BVPs Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems [Volume 10, Issue 4, 2022, Pages 942-953]
Singularly perturbed parabolic convection-diffusion problem Parameter-uniform robust scheme for singularly perturbed parabolic convection-diffusion problems with large time-lag [Volume 10, Issue 4, 2022, Pages 954-968]
Singularly perturbed problem A Robust computational method for singularly perturbed delay parabolic convection-diffusion equations arising in the modeling of neuronal variability [Volume 10, Issue 2, 2022, Pages 475-488]
Singularly perturbed problem Uniformly convergent fitted operator method for singularly perturbed delay differential equations [Volume 10, Issue 2, 2022, Pages 502-518]
Soliton solution Obtaining soliton solutions of equations combined with the Burgers and equal width wave equations using a novel method [Volume 10, Issue 3, 2022, Pages 826-836]
Soliton solutions An effective technique for the conformable space-time fractional cubic-quartic nonlinear Schrodinger equation with different laws of nonlinearity [Volume 10, Issue 3, 2022, Pages 701-715]
Soliton wave solution Some new soliton solutions for the nonlinear the fifth-order integrable equations [Volume 10, Issue 2, 2022, Pages 445-460]
Space time fractional Klein-Gordon equation Exact solutions of the space time-fractional Klein-Gordon equation with cubic nonlinearities using some methods [Volume 10, Issue 3, 2022, Pages 674-685]
Spectral boundary condition The interior inverse boundary value problem for the impulsive Sturm-Liouville operator with the spectral boundary conditions [Volume 10, Issue 2, 2022, Pages 519-525]
Spectrum The interior inverse boundary value problem for the impulsive Sturm-Liouville operator with the spectral boundary conditions [Volume 10, Issue 2, 2022, Pages 519-525]
Square interpolation Approximate price of the option under discretization by applying fractional quadratic interpolation [Volume 10, Issue 4, 2022, Pages 1075-1085]
Squeeze parameter Application of variation of parameter’s method for hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates [Volume 10, Issue 3, 2022, Pages 580-594]
SSPRK scheme Numerical solution of the hyperbolic telegraph equation using cubic B-spline-based differential quadrature of high accuracy [Volume 10, Issue 4, 2022, Pages 837-859]
Stability A new numerical fractional differentiation formula to approximate the Caputo-Fabrizio fractional derivative: error analysis and stability [Volume 10, Issue 1, 2022, Pages 12-27]
Stability Optimal control of satellite attitude and its stability based on quaternion parameters [Volume 10, Issue 1, 2022, Pages 168-178]
Stability Analysis of non-hyperbolic equilibria for Caputo fractional system [Volume 10, Issue 2, 2022, Pages 298-306]
Stability analysis Modulation instability analysis, optical solitons and other solutions to the (2+1)-dimensional hyperbolic nonlinear Schrodinger’s equation [Volume 10, Issue 1, 2022, Pages 179-190]
Stenosis Study of the non-Newtonian behaviour of Reiner Rivlin relative to power law in arterial stenosis [Volume 10, Issue 4, 2022, Pages 928-941]
Stochastic analysis A simulation study of the COVID-19 pandemic based on the Ornstein-Uhlenbeck processes [Volume 10, Issue 3, 2022, Pages 738-745]
Stochastic differential equations The convergence of exponential Euler method for weighted fractional stochastic equations [Volume 10, Issue 2, 2022, Pages 538-548]
Stochastic differential equations Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations [Volume 10, Issue 3, 2022, Pages 617-638]
Stochastic process A numerical technique for solving nonlinear fractional stochastic integro-differential equations with n-dimensional Wiener process [Volume 10, Issue 1, 2022, Pages 61-76]
Stochastic Runge-Kutta schemes Mean-square stability of a constructed Third-order stochastic Runge–Kutta schemes for general stochastic differential equations [Volume 10, Issue 3, 2022, Pages 617-638]
Sturm-Liouville operator with the impulse The interior inverse boundary value problem for the impulsive Sturm-Liouville operator with the spectral boundary conditions [Volume 10, Issue 2, 2022, Pages 519-525]
Sumudu transform Regularized Prabhakar derivative for partial differential equations [Volume 10, Issue 3, 2022, Pages 726-737]
Superinfection Backward bifurcation in a two strain model of heroin addiction [Volume 10, Issue 3, 2022, Pages 656-673]
System of differential equations Combining the reproducing kernel method with a practical technique to solve the system of nonlinear singularly perturbed boundary value problems [Volume 10, Issue 4, 2022, Pages 942-953]

T

The (1/G0)-expansion method On exact solutions of the generalized Pochhammer-Chree equation [Volume 10, Issue 3, 2022, Pages 746-754]
The exp-function approach Optical Solitons and Rogue wave solutions of NLSE with variables coefficients and modulation instability analysis [Volume 10, Issue 4, 2022, Pages 905-913]
The (G0/G)-expansion method New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution [Volume 10, Issue 1, 2022, Pages 158-167]
The generalized Pochhammer-Chree equation On exact solutions of the generalized Pochhammer-Chree equation [Volume 10, Issue 3, 2022, Pages 746-754]
Thermal Analysis Studying the thermal analysis of rectangular cross section porous fin: A numerical approach [Volume 10, Issue 2, 2022, Pages 338-350]
The Thin-film Ferroelectric Materials equation New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution [Volume 10, Issue 1, 2022, Pages 158-167]
The variational iteration method New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution [Volume 10, Issue 1, 2022, Pages 158-167]
Time fractional Black-Scholes model Approximate price of the option under discretization by applying fractional quadratic interpolation [Volume 10, Issue 4, 2022, Pages 1075-1085]
Time fractional parabolic partial differential equations Numerical solution for solving fractional parabolic partial differential equations [Volume 10, Issue 1, 2022, Pages 121-143]
Transaction cost Exact solutions and numerical simulation for Bakstein-Howison model [Volume 10, Issue 2, 2022, Pages 461-474]
Transport of flow and heat transfer Application of variation of parameter’s method for hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates [Volume 10, Issue 3, 2022, Pages 580-594]
Travelling wave New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution [Volume 10, Issue 1, 2022, Pages 158-167]

U

Universal approximation properties Application of fuzzy systems on the numerical solution of the elliptic PDE-constrained optimal control problems [Volume 10, Issue 2, 2022, Pages 351-371]
Unstable nonlinear fractional-order Schrödinger equation Dynamics of combined soliton solutions of unstable nonlinear fractional-order Schrödinger equation by beta-fractional derivative [Volume 10, Issue 2, 2022, Pages 549-566]

V

Variation of parameter’s method Application of variation of parameter’s method for hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates [Volume 10, Issue 3, 2022, Pages 580-594]
Velocity profile and thermal profile Application of variation of parameter’s method for hydrothermal analysis on MHD squeezing nanofluid flow in parallel plates [Volume 10, Issue 3, 2022, Pages 580-594]
Viscosity Study of the non-Newtonian behaviour of Reiner Rivlin relative to power law in arterial stenosis [Volume 10, Issue 4, 2022, Pages 928-941]
Volterra-Fredholm integral equation Shifted Jacobi collocation method for Volterra-Fredholm integral equation [Volume 10, Issue 2, 2022, Pages 408-418]
Von-Neumann stability analysis An optimal B-spline collocation technique for numerical simulation of viscous coupled Burgers’ equation [Volume 10, Issue 4, 2022, Pages 1027-1045]

W

Weighted fractional Brownian motion The convergence of exponential Euler method for weighted fractional stochastic equations [Volume 10, Issue 2, 2022, Pages 538-548]