Compact implicit integration factor method for the nonlinear Dirac equation (Q1784871)

A numerical method of high accuracy is treated, for the solution of the \((1+1)\)-dimensional nonlinear Dirac (NLD) equation. The authors use a compact finite difference method (CM) with space discretization and obtain a nonlinear ordinary differential system, and then they use for the time discretization the implicit integration factor method (IIF) to this system. Mainly, they introduce CM-IIF4 of 4th-order scheme in both space and time. Numerical examples are given to confirm the accuracy of these schemes and to study the interaction dynamics of two NLD solitary waves.