Stable and efficient time second-order difference schemes for fractional Klein–Gordon–Zakharov system

Abstract

In this paper, we develop and analyze two stable and efficient time second-order difference schemes for space fractional Klein–Gordon–Zakharov (KGZ) system. The former is based on the multi-point weighted time second-order scheme to construct energy conservative linearized difference scheme. The latter is on the basis of time second-order splitting technique to develop accurate, efficient, linear and decoupled difference scheme. A main idea of the latter is to split the original fractional KGZ system into linear and nonlinear parts, and then to advance the subproblems with three stages. Furthermore, by utilizing the cut-off technique, energy analysis method and mathematical induction method, we obtain the error estimates of the former scheme, without any restrictive conditions on the grid ratio, compared with the restrictive conditions demanded in the existing literature. The feature of proposed schemes are linear decoupled, and easy to be applied in parallel computing, especially in long time simulations. At last, some numerical results are provided to validate the accuracy and efficiency of the proposed schemes, and simulate wave dynamics and interaction of the fractional KGZ system in one and two dimensions.