Convergence of time-splitting energy-conserved symplectic schemes for 3D Maxwell’s equations

Abstract

We propose two symplectic and two non-symplectic schemes for 3D Maxwell’s equations based on the exponential operator splitting technique and Fourier pseudo-spectral method. These schemes are efficient and unconditionally stable, and also preserve four discrete energy conservation laws simultaneously. The error estimates of the schemes are obtained by using some special techniques and the energy method. Numerical results confirm the theoretical analysis. The numerical comparison with some existing methods show the good performance of the proposed schemes.