Compact Implicit Integration Factor Method for the Nonlinear Dirac Equation

Abstract

A high-order accuracy numerical method is proposed to solve the (1 + 1)-dimensional nonlinear Dirac equation in this work. We construct the compact finite difference scheme for the spatial discretization and obtain a nonlinear ordinary differential system. For the temporal discretization, the implicit integration factor method is applied to deal with the nonlinear system. We therefore develop two implicit integration factor numerical schemes with full discretization, one of which can achieve fourth-order accuracy in both space and time. Numerical results are given to validate the accuracy of these schemes and to study the interaction dynamics of the nonlinear Dirac solitary waves.

High-order compact methods for the nonlinear Dirac equation

“…In Bao et al (2016), studied the Crank-Nicolson method, exponential wave integrator Fourier pseudospectral method and time-splitting Fourier pseudospectral method for the NLD equation. In 2017, we discussed some time-splitting methods with charge conservation in Li et al (2017b) and Zhang and Li (2017) studied the compact implicit integration factor method for the nonlinear Dirac equation.…”