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

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-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.

• Keywords

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

35R11, 26A33, 35A35, 65M12

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