结合非标准与紧致有限差分格式求解FitzHugh-Nagumo方程的高阶解

IF 2.4 2区 数学 Q1 MATHEMATICS, APPLIED
Zhi-Chen Li , Yang-Wen Yu , Xiao-Yu Zhang , Qing Fang
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引用次数: 0

摘要

本文提出了一种结合非标准有限差分格式和高阶紧致有限差分格式求解FitzHugh-Nagumo方程的新数值方法。通过严格的数学分析,我们证明了我们的方法的稳定性和收敛性,揭示了不稳定性只在极其罕见的条件下出现。为了验证该方案的有效性,我们通过将数值结果与精确解进行比较,计算了l2和l∞误差以及收敛速度。实验表明,该组合方案在保证稳定性的同时,在保持高阶收敛性的同时,误差最小。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A higher-order solver for the FitzHugh-Nagumo equation by combining nonstandard and compact finite difference scheme
This study presents a novel numerical method for solving the FitzHugh-Nagumo equation by combining nonstandard finite difference (NSFD) and high-order compact finite difference schemes. Through rigorous mathematical analysis, we demonstrate the stability and convergence of our approach, revealing that instability arises only under extremely rare conditions. To verify the efficiency of our scheme, we calculated the l2 and l errors as well as the convergence rate by comparing the numerical results with the exact solution. Experiments show that our combined scheme not only ensures stability, but also possesses the lowest error while maintaining high order convergence.
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来源期刊
Applied Numerical Mathematics
Applied Numerical Mathematics 数学-应用数学
CiteScore
5.60
自引率
7.10%
发文量
225
审稿时长
7.2 months
期刊介绍: The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.
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