A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations

A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations

Year:    2019

Author:    Yao Shi, Qiang Ma, Xiaohua Ding

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1219–1247

Abstract

In this paper, we study a fourth-order quasi-compact conservative difference scheme for solving the fractional Klein-Gordon-Schrödinger equations. The scheme constructed in this work can preserve exactly the discrete charge and energy conservation laws under Dirichlet boundary conditions. By the energy method, the proposed quasi-compact conservative difference scheme is proved to be unconditionally stable and convergent with order $\mathcal{O}(\tau^{2}+h^{4})$ in maximum norm. Finally, several numerical examples are given to confirm the theoretical results.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0157

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 5 : pp. 1219–1247

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Fractional Klein-Gordon-Schrödinger equations Riesz fractional derivative conservative scheme stability convergence.

Author Details

Yao Shi

Qiang Ma

Xiaohua Ding

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