数学
Dirac(视频压缩格式)
非线性系统
克莱恩-戈登方程
索波列夫空间
时域有限差分法
张量(固有定义)
有限差分
应用数学
趋同(经济学)
有限差分法
狄拉克方程
数值分析
数学分析
维数(图论)
纯数学
量子力学
数学物理
物理
经济
中微子
经济增长
作者
Wenfan Yi,Yongyong Cai
出处
期刊:Ima Journal of Numerical Analysis
日期:2018-12-05
卷期号:40 (2): 1266-1293
被引量:12
标识
DOI:10.1093/imanum/dry084
摘要
Abstract We propose and analyze finite difference methods for solving the Klein–Gordon–Dirac (KGD) system. Due to the nonlinear coupling between the complex Dirac ‘wave function’ and the real Klein–Gordon field, it is a great challenge to design and analyze numerical methods for KGD. To overcome the difficulty induced by the nonlinearity, four implicit/semi-implicit/explicit finite difference time domain (FDTD) methods are presented, which are time symmetric or time reversible. By rigorous error estimates, the FDTD methods converge with second-order accuracy in both spatial and temporal discretizations, and numerical results in one dimension are reported to support our conclusion. The error analysis relies on the energy method, the special nonlinear structure in KGD and the mathematical induction. Thanks to tensor grids and discrete Sobolev inequalities, our approach and convergence results are valid in higher dimensions under minor modifications.
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