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

DOI10.1007/s11071-021-06249-xzbMath1517.35206OpenAlexW3127884550MaRDI QIDQ6174325

Ahmed S. Hendy, Mahmoud A. Zaky

Publication date: 16 August 2023

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-021-06249-x

zbMATH Keywords

Galerkin spectral methodnonsmooth solutionsgeneralized time-space-fractional Schrödinger equationsgraded mesh schemes

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) NLS equations (nonlinear Schrödinger equations) (35Q55) Fractional partial differential equations (35R11)

Related Items (10)

Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes ⋮ An accurate computational method for two-dimensional (2D) fractional Rayleigh-Stokes problem for a heated generalized second grade fluid via linear barycentric interpolation method ⋮ Long time behavior of Robin boundary sub-diffusion equation with fractional partial derivatives of Caputo type in differential and difference settings ⋮ Efficient numerical algorithms of time fractional telegraph‐type equations involving Hadamard derivatives ⋮ Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian ⋮ The non-uniform L1-type scheme coupling the finite volume method for the time-space fractional diffusion equation with variable coefficients ⋮ Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain ⋮ A Galerkin meshless reproducing kernel particle method for numerical solution of neutral delay time-space distributed-order fractional damped diffusion-wave equation ⋮ An efficient hybrid numerical scheme for nonlinear multiterm Caputo time and Riesz space fractional-order diffusion equations with delay ⋮ An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion-reaction equations with fixed delay

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