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.
Highlights
It is well known that the Dirac equation plays a fundamental role in relativistic quantum physics [1]
Motivated by the previous work, we propose two compact implicit integration factor (IIF) schemes with high accuracy to solve the (1 + 1)-dimensional nonlinear Dirac (NLD) equation numerically
Numerical examples are given to validate the accuracy of the numerical schemes proposed in Section 4, that is, compact finite difference (CM)-IIF2 scheme and CM-IIF4 scheme
Summary
It is well known that the Dirac equation plays a fundamental role in relativistic quantum physics [1]. There has been a worldwide wave of interest in efficient and high-order numerical simulations for the NLD equation. Motivated by the previous work, we propose two compact implicit integration factor (IIF) schemes with high accuracy to solve the (1 + 1)-dimensional NLD equation numerically. To this end, the fourth-order compact finite difference (CM) scheme is applied to discretize the NLD equation in spatial direction.
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