High-order conservative schemes for the space fractional nonlinear Schrödinger equation

DOI10.1016/j.apnum.2021.02.017zbMath1475.65084OpenAlexW3134120915MaRDI QIDQ2029123

Junjie Wang

Publication date: 3 June 2021

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.02.017

zbMATH Keywords

convergenceconservation lawfractional Schrödinger equationhigh-order conservative scheme

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) Extrapolation to the limit, deferred corrections (65B05) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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High-order conservative scheme for the coupled space fractional nonlinear Schrödinger equations ⋮ A local scheme for numerical simulation of multi-dimensional dynamic quantum model: application to decision-making ⋮ Efficient eighth‐order accurate energy‐preserving compact difference schemes for the coupled Schrödinger–Boussinesq equations ⋮ Structure-preserving scheme for one dimension and two dimension fractional KGS equations ⋮ An operator splitting method for multi-asset options with the Feynman-Kac formula ⋮ Numerical analysis of a fourth-order linearized difference method for nonlinear time-space fractional Ginzburg-Landau equation ⋮ A sharp version of Phragmén-Lindelöf type theorem for the stationary Schrödinger equation

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