Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation

DOI10.1007/s11075-020-01044-yzbMath1496.65174OpenAlexW3119860031MaRDI QIDQ2048836

Ying Wang, Liquan Mei, Gang Wang, Linlin Bu

Publication date: 24 August 2021

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-020-01044-y

zbMATH Keywords

unconditional stabilityoptimal error estimatesnonlinear time-fractional Schrödinger equation

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (9)

Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes ⋮ A second-order finite difference scheme for the multi-dimensional nonlinear time-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 ⋮ Space-time methods based on isogeometric analysis for time-fractional Schrödinger equation ⋮ A second-order \(L2\)-\(1_\sigma\) difference scheme for the nonlinear time-space fractional Schrödinger equation ⋮ Optimal error analysis of the alikhanov formula for a time-fractional Schrödinger equation ⋮ Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation ⋮ Fast L2-1\(_\sigma\) Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives

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