An analysis of implicit conservative difference solver for fractional Klein–Gordon–Zakharov system

Abstract

In this paper, we propose an efficient linearly implicit conservative difference solver for the fractional Klein–Gordon–Zakharov system. First of all, we present a detailed derivation of the energy conservation property of the system in the discrete setting. Then, by using the mathematical induction, it is proved that the proposed scheme is uniquely solvable. Subsequently, by virtue of the discrete energy method and a ‘cut-off’ function technique, it is shown that the proposed solver possesses the convergence rates of O(Δt2+h2) in the sense of L∞- and L2- norms, respectively, and is unconditionally stable. Finally, numerical results testify the effectiveness of the proposed scheme and exhibit the correctness of theoretical results.