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

Yao Shi ,  Qiang Ma and Xiaohua Ding

10.4208/aamm.OA-2018-0157

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

Preview Full PDF BiBTex 6 431
  • Abstract

In this paper, we study a fourth-order quasi-compact conservative difference scheme for solving the fractional Klein-Gordon-Schrodinger 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.

  • History

Published online: 2019-06

  • AMS Subject Headings

35R11, 26A33, 35A35, 65M12

  • Cited by