Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations

DOI10.1007/s42985-020-00048-6zbMath1460.35306OpenAlexW3096721603WikidataQ115370375 ScholiaQ115370375MaRDI QIDQ2659811

Yanyan Li

Publication date: 26 March 2021

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42985-020-00048-6

zbMATH Keywords

discrete sine transformmatrix transfer techniquetime-stepping methodsspace-fractional nonlinear Schrödinger equations

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) Numerical methods for discrete and fast Fourier transforms (65T50) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (4)

An efficient fourth-order accurate conservative scheme for Riesz space fractional Schrödinger equation with wave operator ⋮ Efficient eighth‐order accurate energy‐preserving compact difference schemes for the coupled Schrödinger–Boussinesq equations ⋮ A fast implicit difference scheme for solving high-dimensional time-space fractional nonlinear Schrödinger equation ⋮ A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations

Cites Work

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• Maximum-norm error analysis of a difference scheme for the space fractional CNLS
• A linearly implicit conservative difference scheme for the space fractional coupled nonlinear Schrödinger equations
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
• New numerical methods for the Riesz space fractional partial differential equations
• Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems
• Functional spaces for the theory of elliptic partial differential equations. Transl. from the French by Reinie Erné
• Exponential time differencing for stiff systems
• Generalized integrating factor methods for stiff PDEs
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• A new class of time discretization schemes for the solution of nonlinear PDEs
• Fractional quantum mechanics and Lévy path integrals
• Schrödinger equations with fractional Laplacians
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• A comparative study on nonlocal diffusion operators related to the fractional Laplacian
• Split-step alternating direction implicit difference scheme for the fractional Schrödinger equation in two dimensions
• Parallel methods and higher dimensional NLS equations
• Fourth-order compact schemes for the numerical simulation of coupled Burgers' equation
• A fourth-order explicit schemes for the coupled nonlinear Schrödinger equation
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations
• Soliton dynamics for fractional Schrödinger equations
• Global Well-Posedness for the Fractional Nonlinear Schrödinger Equation
• Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
• Attainable order of rational approximations to the exponential function with only real poles
• A Fourth-order Compact ADI scheme for Two-Dimensional Nonlinear Space Fractional Schrödinger Equation
• Collocation method for fractional quantum mechanics

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