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.
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