A class of linearized energy-conserved finite difference schemes for nonlinear space-fractional Schrödinger equations

DOI10.1080/00207160.2015.1009904zbMath1338.65217OpenAlexW2027470594MaRDI QIDQ2804917

Zheng Yang

Publication date: 6 May 2016

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2015.1009904

zbMATH Keywords

stabilityconvergencenumerical exampleenergy conservationfinite difference schemesshifted Grünwald-Letnikov formulafractional central differencenonlinear space-fractional Schrödinger equationsweighted shifted Grünwald-Letnikov formulas

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Fractional partial differential equations (35R11)

Related Items (11)

Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation ⋮ An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations ⋮ Bounded solutions of second order of accuracy difference schemes for semilinear fractional Schrödinger equations ⋮ A conservative difference scheme with optimal pointwise error estimates for two‐dimensional space fractional nonlinear Schrödinger equations ⋮ Two competent novel techniques based on two-dimensional wavelets for nonlinear variable-order Riesz space-fractional Schrödinger equations ⋮ A high-order nodal discontinuous Galerkin method for nonlinear fractional Schrödinger type equations ⋮ A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations ⋮ Numerical simulation of multi-dimensional distributed-order generalized Schrödinger equations ⋮ A conservative numerical method for the fractional nonlinear Schrödinger equation in two dimensions ⋮ A relaxation-type Galerkin FEM for nonlinear fractional Schrödinger equations ⋮ Implicit-Explicit Difference Schemes for Nonlinear Fractional Differential Equations with Nonsmooth Solutions

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