Time-Compact Scheme for the One-Dimensional Dirac Equation

Based on the Lie-algebra, a new time-compact scheme is proposed to solve the one-dimensional Dirac equation. This time-compact scheme is proved to satisfy the conservation of discrete charge and is unconditionally stable. The time-compact scheme is of fourth-order accuracy in time and spectral order accuracy in space. Numerical examples are given to test our results.

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