A linear, symmetric and energy-conservative scheme for the space-fractional Klein-Gordon-Schrödinger equations

DOI10.1016/j.aml.2019.03.032zbMath1478.65099OpenAlexW2925871920MaRDI QIDQ2274714

Yanyan Li

Publication date: 1 October 2019

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

Full work available at URL: https://doi.org/10.1016/j.aml.2019.03.032

zbMATH Keywords

energy conservationCrank-Nicolson methodFourier spectral methodinvariant energy quadratization approachspace-fractional Klein-Gordon-Schrödinger equations

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (14)

Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schrödinger system with fractional Laplacian in unbounded domains ⋮ A linearized conservative Galerkin-Legendre spectral method for the strongly coupled nonlinear fractional Schrödinger equations ⋮ Fully-discrete energy-preserving scheme for the space-fractional Klein-Gordon equation via Lagrange multiplier type scalar auxiliary variable approach ⋮ A dissipation-preserving finite-difference scheme for a generalized Higgs boson equation in the de Sitter space-time ⋮ Efficient energy-preserving finite difference schemes for the Klein-Gordon-Schrödinger equations ⋮ Second-order linear adaptive time-stepping schemes for the fractional Allen-Cahn equation ⋮ Mass-, and energy preserving schemes with arbitrarily high order for the Klein-Gordon-Schrödinger equations ⋮ A numerical investigation with energy-preservation for nonlinear space-fractional Klein-Gordon-Schrödinger system ⋮ On the dissipativity of some Caputo time-fractional subdiffusion models in multiple dimensions: theoretical and numerical investigations ⋮ A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator ⋮ A family of effective structure-preserving schemes with second-order accuracy for the undamped sine-Gordon equation ⋮ Theoretical analysis of an explicit energy-conserving scheme for a fractional Klein-Gordon-Zakharov system ⋮ On high-order schemes for tempered fractional partial differential equations ⋮ Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation

Cites Work

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• Unconditional and optimal \(H^2\)-error estimates of two linear and conservative finite difference schemes for the Klein-Gordon-Schrödinger equation in high dimensions
• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• A series of new explicit exact solutions for the coupled Klein-Gordon-Schrödinger equations
• A numerically efficient and conservative model for a Riesz space-fractional Klein-Gordon-Zakharov system
• Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
• Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations
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• Analysis and Approximation of a Fractional Cahn--Hilliard Equation
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• Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
• A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

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