A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation

DOI10.1016/j.apnum.2020.03.004zbMath1436.65099OpenAlexW3010014136MaRDI QIDQ1986169

Mingfa Fei, Xiaohua Ma, Nan Wang, Cheng-Ming Huang

Publication date: 7 April 2020

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2020.03.004

zbMATH Keywords

convergenceunique solvabilityCaputo derivativeRiesz fractional derivative\(L2- 1_\sigma\) formulatime-space fractional Schrödinger equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (8)

Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes ⋮ A linearized conservative Galerkin-Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations ⋮ Convergence analysis of a fast second‐order time‐stepping numerical method for two‐dimensional nonlinear time–space fractional Schrödinger equation ⋮ Linearized fast time-stepping schemes for time-space fractional Schrödinger equations ⋮ A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation ⋮ Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation ⋮ A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation ⋮ Conservative Numerical Schemes for the Nonlinear Fractional Schrödinger Equation

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