非线性系统
积分器
狄拉克方程
数学
Dirac(视频压缩格式)
趋同(经济学)
不动点迭代
应用数学
数学物理
克莱恩-戈登方程
数学分析
迭代法
狄拉克算符
指数函数
物理
固定点
量子力学
数学优化
经济增长
经济
电压
中微子
出处
期刊:Multiscale Modeling & Simulation
[Society for Industrial and Applied Mathematics]
日期:2022-02-22
卷期号:20 (1): 164-187
被引量:2
摘要
We propose a class of efficient and uniformly accurate nested Picard iterative integrators (NPI) for solving the nonlinear Dirac equation (NLDE) in the nonrelativistic regime, and apply it to study the convergence rates of the NLDE to its limiting models, the dynamics of traveling waves, and the two-dimensional dynamics. The NLDE involves a dimensionless parameter $\varepsilon\in (0, 1]$, and its solution is highly oscillatory in time with wavelength $O(\varepsilon^2)$ in the nonrelativistic regime. To gain uniform accuracies in time, the NPI method employs an operator decomposition technique for explicitly separating the highly oscillatory phases and utilizes exponential wave integrators for the time integrals. Moreover, with the help of nested Picard iterations, the NPI method could easily achieve uniform first- and second-order accuracies.
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