Convergence analysis of two conservative finite difference fourier pseudo-spectral schemes for klein-Gordon-Dirac system

Abstract

In this paper, we propose and study two conservative finite difference Fourier pseudo-spectral schemes numerically solving the Klein-Gordon-Dirac (KGD) system with periodic boundary conditions. The resulting numerical schemes are time symmetric and proved to conserve the discrete mass and the discrete energy. We give a rigorously convergence analysis for the schemes. Specifically, we establish the error estimates which are without any restrictions (CFL condition) on the ratio of time step to space step. The convergence rates of the new schemes are proved to be the temporal second-order and spatial spectral-order, respectively, in a Hm-norm. The main proof tools include the ideas of standard mathematical induction and the method of defining energy. Finally, we give the numerical experiments to support our theoretical analysis and error bounds.