Implicit integration factor method for the nonlinear Dirac equation

Abstract

A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac (NLD) equation. Based on the implicit integration factor (IIF) method, two schemes are proposed. Central differences are applied to the spatial discretization. The semi-discrete scheme keeps the conservation of the charge and energy. For the temporal discretization, second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization. Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.