An explicit numerical scheme for the Sine-Gordon equation in 2+1 dimensions

A. G. Bratsos
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Abstract

The paper presents an explicit finite-difference method for the numerical solution of the Sine-Gordon equation in two space variables, as it arises, for example, in rectangular large-area Josephson junction. The dispersive nonlinear partial differential equation of the system allows for soliton-type solutions, an ubiquitous phenomenon in a large-variety of physical problems.

The method, which is based on fourth order rational approximants of the matrix-exponential term in a three-time level recurrence relation, after the application of finite-difference approximations, it leads finally to a second order initial value problem. Because of the existing sinus term this problem becomes nonlinear. To avoid solving the arising nonlinear system a new method based on a predictor-corrector scheme is applied. Both the nonlinear method and the predictor-corrector are analyzed for local truncation error, stability and convergence. Numerical solutions for cases involving the most known from the bibliography ring and line solitons are given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

2+1维中sin - gordon方程的显式数值格式
本文给出了两个空间变量中正弦-戈登方程数值解的显式有限差分法,例如矩形大面积Josephson结。系统的色散非线性偏微分方程允许孤子型解,这是在各种物理问题中普遍存在的现象。该方法基于三阶递归关系中矩阵-指数项的四阶有理近似,在应用有限差分近似后,最终得到二阶初值问题。由于窦项的存在,这个问题变得非线性。为了避免求解产生的非线性系统,采用了一种基于预测-校正格式的新方法。分析了非线性方法和预测校正方法的局部截断误差、稳定性和收敛性。给出了文献中最常见的环孤子和线孤子的数值解。(©2005 WILEY-VCH Verlag GmbH &KGaA公司,Weinheim)
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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