Numerical Methods for the Nonlinear Dirac Equation in the Massless Nonrelativistic Regime
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS(2024)
摘要
Numerical methods for the nonlinear Dirac equation (NDE) in the massless nonrelativistic regime are considered. In this regime, the equation contains a small dimensionless parameter 0 < epsilon <= 1, and its solution is highly oscillatory in time. We present and analyze traditional numerical schemes for the NDE, including finite difference methods, time-splitting methods and exponential integrators. Error analysis indicates that all these methods require an epsilon-dependent time-step size to achieve an optimal convergence order. Utilizing an operator splitting technique, we propose a uniformly accurate (UA) scheme. The scheme enables first-order convergence in time for all epsilon is an element of (0,1] without restrictions on time-step size. Error estimates for the UA scheme are rigorously established and numerical results confirm the properties of the method.
更多查看译文
关键词
Nonlinear Dirac equation,uniformly accurate,finite difference method,time-splitting method,exponential integrator
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要