Volume 11, Issue 5
A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations

Yao Shi, Qiang Ma & Xiaohua Ding

Adv. Appl. Math. Mech., 11 (2019), pp. 1219-1247.

Published online: 2019-06

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  • 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.

  • Keywords

Fractional Klein-Gordon-Schrodinger equations, Riesz fractional derivative, conservative scheme, stability, convergence.

  • AMS Subject Headings

35R11, 26A33, 35A35, 65M12

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COPYRIGHT: © Global Science Press

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@Article{AAMM-11-1219, author = {}, title = {A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0157}, url = {http://global-sci.org/intro/article_detail/aamm/13208.html} }
TY - JOUR T1 - A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1219 EP - 1247 PY - 2019 DA - 2019/06 SN - 11 DO - http://dor.org/10.4208/aamm.OA-2018-0157 UR - https://global-sci.org/intro/article_detail/aamm/13208.html KW - Fractional Klein-Gordon-Schrodinger equations, Riesz fractional derivative, conservative scheme, stability, convergence. AB -

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.

Yao Shi, Qiang Ma & Xiaohua Ding. (2019). A New Energy-Preserving Scheme for the Fractional Klein-Gordon-Schrödinger Equations. Advances in Applied Mathematics and Mechanics. 11 (5). 1219-1247. doi:10.4208/aamm.OA-2018-0157
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