Two energy-preserving Fourier pseudo-spectral methods and error estimate for the Klein–Gordon–Dirac system

Abstract

We devote the present paper to the convergency of conservative Fourier pseudo-spectral methods for three-dimensional Klein–Gordon–Dirac (KGD) system. By adopting the mathematical induction argument, standard energy method and inverse inequality, the error bound is established under the condition τ<h with time step τ and mesh size h. More specifically, the scalar ϕ and 4-spinor ψ are proved to be convergent in H2 and H1-norm, respectively. In addition, we establish a frame to compute the numerical solutions of three-dimensional KGD system with periodic conditions, and a faster solver is designed to accelerate the computation by means of orthogonal diagonalization technique. Numerical results are reported to verify the error estimate and discrete conservation laws.