Operator-Compensation Schemes Combining with Implicit Integration Factor Method for the Nonlinear Dirac Equation

Abstract

Abstract A high-order accuracy numerical method for the (1+1)-dimensional nonlinear Dirac (NLD) equation is given in this work. For the spatial discretization, high-order operator-compensation technology is adopted, then semi-discrete scheme is obtained. Energy conservation and charge conservation are shown for the semi- discrete scheme. For the temporal discretization, implicit integration factor ( IIF) method is utilized to deal with the ordinary differential equations that are obtained from the semi-discrete scheme. The accuracy of the high-order numerical method is verified by numerical experiments, and the interaction dynamics of NLD solitary waves are investigated.