Structure-preserving compact ADI schemes for the space fractional Klein-Gordon-Schrödinger equations and the dynamic simulation of solitary wave solutions

Abstract

In this study, we introduce a novel structure-preserving compact alternating direction implicit (ADI) difference scheme based on the BDF2-θ and the ADI algorithm for solving the space fractional Klein-Gordon-Schrödinger equations. The primary focus of this article lies in the theoretical analysis and computational efficiency of the proposed schemes, which encompasses rigorous proofs of the error estimation, stability, and approximate conservation laws. Furthermore, we provide a comprehensive exposition on the implementation of these schemes, detailing their efficient execution. Comparative analysis of numerical simulations reveal the role of the fractional parameters for the solitary wave solutions and check the feasibility of the constructed new structure-preserving schemes.