A sixth-order compact time-splitting Fourier pseudospectral method

TL;DR

This paper introduces a new sixth-order compact time-splitting Fourier pseudospectral method for solving the Dirac equation, offering improved accuracy and efficiency, especially in nonrelativistic regimes without magnetic potentials.

Contribution

The paper presents a novel sixth-order compact time-splitting scheme that simplifies implementation and enhances computational efficiency for the Dirac equation, extending to time-dependent potentials.

Findings

Significant accuracy and efficiency improvements over existing methods.

Maintains super-resolution property in nonrelativistic regimes.

Effective for problems without external magnetic potentials.

Abstract

In this paper, we propose a novel sixth-order compact time-splitting scheme, denoted as $ S_{6\text{c}}$, for solving the Dirac equation in the absence of external magnetic potentials. This method is easy to implement, and it provides a substantial reduction in computational complexity compared to the existing sixth-order splitting schemes. By incorporating a time-ordering technique, we also extend $S_{6\text{c}}$ to address problems with time-dependent potentials. Comprehensive comparisons with various time-splitting methods show that $S_{6\text{c}}$ exhibits significant advantages in terms of both precision and efficiency. Moreover, numerical results indicate that $S_{6\text{c}}$ maintains the super-resolution property for the Dirac equation in the nonrelativistic regime in the absence of external magnetic potentials.