Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

An alternating direction implicit legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation

(2022) Yanqin Liu et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

An energy-preserving computational approach for the semilinear space fractional damped Klein–Gordon equation with a generalized scalar potential

(2022) Ahmed S. Hendy et al.   APPLIED MATHEMATICAL MODELLING

An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function

(2022) A.K. Omran et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra–Fredholm integral equations

(2021) Nermeen A Elkot et al.   COMMUNICATIONS IN THEORETICAL PHYSICS

Alikhanov Legendre—Galerkin Spectral Method for the Coupled Nonlinear Time-Space Fractional Ginzburg–Landau Complex System

(2021) Mahmoud A. Zaky et al.   Mathematics

Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

(2021) Ahmed S. Hendy et al.   NONLINEAR DYNAMICS

The impact of memory effect on space fractional strong quantum couplers with tunable decay behavior and its numerical simulation

(2021) Ahmed S. Hendy et al.   Scientific Reports

Computational aspects of fractional Romanovski–Bessel functions

(2021) Howayda Abo-Gabal et al.   COMPUTATIONAL & APPLIED MATHEMATICS

Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain

(2021) Xiaoqing Chi et al.   APPLIED MATHEMATICS AND COMPUTATION

Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems

(2021) Harendra Singh   INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION

Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative

(2021) Ibrahem G. Ameen et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations

(2021) Mahmoud A. Zaky et al.   NUMERICAL ALGORITHMS

Crank-Nicolson/finite element approximation for the Schrödinger equation in the de Sitter spacetime

(2021) Harun Selvitopi et al.   PHYSICA SCRIPTA

Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain

(2021) Hui Zhang et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions

(2021) Ramy M. Hafez et al.   MATHEMATICS AND COMPUTERS IN SIMULATION

Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay

(2021) Sarita Nandal et al.   Mathematics

A novel Jacob spectral method for multi-dimensional weakly singular nonlinear Volterra integral equations with nonsmooth solutions

(2020) Mahmoud A. Zaky et al.   ENGINEERING WITH COMPUTERS

Semi-implicit Galerkin–Legendre Spectral Schemes for Nonlinear Time-Space Fractional Diffusion–Reaction Equations with Smooth and Nonsmooth Solutions

(2020) Mahmoud A. Zaky et al.   JOURNAL OF SCIENTIFIC COMPUTING

Jacobi Spectral Galerkin Method for Distributed-Order Fractional Rayleigh–Stokes Problem for a Generalized Second Grade Fluid

(2020) Ramy M. Hafez et al.   Frontiers in Physics

Legendre spectral method for the fractional Bratu problem

(2020) Harendra Singh et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions

(2020) Mahmoud A. Zaky   APPLIED NUMERICAL MATHEMATICS

Graded mesh discretization for coupled system of nonlinear multi-term time-space fractional diffusion equations

(2020) Ahmed S. Hendy et al.   ENGINEERING WITH COMPUTERS

Crank–Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation

(2020) Mostafa Abbaszadeh et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Chebyshev spectral methods for multi-order fractional neutral pantograph equations

(2020) S. S. Ezz-Eldien et al.   NONLINEAR DYNAMICS

Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations

(2020) Ahmed S. Hendy et al.   APPLIED NUMERICAL MATHEMATICS

Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations

(2020) Mahmoud A. Zaky et al.   INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

On Romanovski–Jacobi polynomials and their related approximation results

(2020) Howayda Abo‐Gabal et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media

(2020) Harendra Singh   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis

(2020) Mahmoud A. Zaky et al.   APPLIED NUMERICAL MATHEMATICS

An efficient dissipation–preserving Legendre–Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe

(2020) Mahmoud A. Zaky et al.   APPLIED NUMERICAL MATHEMATICS

The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains

(2019) Hao Yu et al.   NUMERICAL ALGORITHMS

Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations

(2019) Mahmoud A. Zaky et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with smooth solutions

(2019) Mahmoud A. Zaky et al.   NUMERICAL ALGORITHMS

Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients

(2019) Harendra Singh et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Solution of multi-dimensional Klein–Gordon–Zakharov and Schrödinger/Gross–Pitaevskii equations via local Radial Basis Functions–Differential Quadrature (RBF–DQ) technique on non-rectangular computational domains

(2018) Mehdi Dehghan et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator

(2018) Xiujun Cheng et al.   Boundary Value Problems

An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations

(2018) Zeting Liu et al.   APPLIED NUMERICAL MATHEMATICS

DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose–Einstein condensates

(2018) Mohammad Ilati et al.   APPLIED MATHEMATICS AND COMPUTATION

Numerical simulation of multi-dimensional distributed-order generalized Schrödinger equations

(2017) A. H. Bhrawy et al.   NONLINEAR DYNAMICS

Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations

(2017) Dongfang Li et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Spectral and pseudospectral approximations for the time fractional diffusion equation on an unbounded domain

(2016) Hu Chen et al.   JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations

(2015) A.H. Bhrawy et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Jacobi–Gauss–Lobatto collocation method for the numerical solution of nonlinear Schrödinger equations

(2014) E.H. Doha et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrödinger equation arising in quantum mechanics

(2013) Akbar Mohebbi et al.   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions

(2013) Tingchun Wang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions

(2013) Xiaodan Zhao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation

(2008) Shu-Sen Xie et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING