Efficient energy-preserving finite difference schemes for the Klein-Gordon-Schrödinger equations

In this study, we construct three efficient and conservative high-order accurate finite difference schemes for solving the Klein-Gordon-Schrödinger equations with homogeneous Dirichlet boundary conditions. The spatial discretization is carried out by a novel fourth-order accurate central difference...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) Vol. 149; pp. 150 - 170
Main Authors: Almushaira, Mustafa, Jing, Yan-Fei
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.11.2023
Subjects:
Central finite difference
Discrete sine transform
Energy-preserving
Klein-Gordon-Schrödinger equations
Scalar auxiliary variable
Scalar auxiliary variable
Central finite difference
Klein-Gordon-Schrödinger equations
Energy-preserving
Discrete sine transform
ISSN:0898-1221, 1873-7668
Online Access:Get full text
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Summary:In this study, we construct three efficient and conservative high-order accurate finite difference schemes for solving the Klein-Gordon-Schrödinger equations with homogeneous Dirichlet boundary conditions. The spatial discretization is carried out by a novel fourth-order accurate central difference scheme in which the fast discrete sine transform can be utilized for efficient implementation. The second-order conservative Crank-Nicolson scheme is considered in the temporal direction. Then a priori estimate, conservation laws, and convergence of the first scheme in two-dimensional space are discussed. A linearized iteration based on the fast discrete sine transform technique is derived to solve the nonlinear system effectively. Because the resultant algorithm does not use matrix inversion, it is computationally efficient in long-time calculations. For comparative purposes, two other schemes are constructed based on improved scalar auxiliary variable approaches by converting the Klein-Gordon-Schrödinger equations into an equivalent new system which involves solving linear systems with constant coefficients at each time step. Moreover, we need to point out that the proposed schemes are decoupled, which makes them appropriate for parallel computation to significantly reduce the computing time. Finally, numerical experiments are presented to validate the correctness of theoretical results and demonstrate the excellent performance in long-time conservation of the schemes.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2023.09.003