FitzHugh-Nagumo方程的二阶无条件不变集保持格式

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-04-17 DOI:10.1016/j.camwa.2025.04.013

Yiyi Liu , Xueqing Teng , Xiaoqiang Yan , Hong Zhang

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引用次数: 0

摘要

本文给出并分析了FitzHugh-Nagumo方程的二阶指数差分龙格-库塔格式（ETDRK2）。利用二阶有限差分空间离散化，我们通过结合稳定技术和时间逼近的ETDRK2方案推导出完全离散的数值格式。给出了FitzHugh-Nagumo方程的最小不变集。我们证明了该方案无条件地保持不变量集，没有任何时间步长约束。验证了该方法在时间和空间上的收敛性，达到了二阶精度。数值实验验证了该方法的有效性、稳定性和保结构性。

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A second-order, unconditionally invariant-set-preserving scheme for the FitzHugh-Nagumo equation

In this paper, we present and analyze a second-order exponential time differencing Runge–Kutta (ETDRK2) scheme for the FitzHugh-Nagumo equation. Utilizing a second-order finite-difference space discretization, we derive the fully discrete numerical scheme by incorporating both the stabilization technique and the ETDRK2 scheme for temporal approximation. The smallest invariant set of the FitzHugh-Nagumo equation is presented. We demonstrate that the proposed scheme unconditionally preserves the invariant set without any time-step constraint. The convergence in both time and space is verified to achieve second-order accuracy. Numerical experiments are carried out to illustrate the efficiency, stability, and structure-preserving property of the proposed scheme.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).