Time‐splitting methods with charge conservation for the nonlinear Dirac equation

Abstract

In this work, four numerical time‐splitting methods are proposed for the (1 + 1)‐dimensional nonlinear Dirac equation. All of these methods (or schemes) are proved to satisfy the charge conservation in the discrete level. To enhance the computation efficiency, the block Thomas algorithm is adopted. Numerical experiments are given to test the accuracy order for these schemes, to simulate numerically the binary collision including two standing waves and two moving solitons, meanwhile, the dynamic properties for the nonlinear Dirac equation are discussed. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1582–1602, 2017