摘要
为解决FitzHugh-Nagumo(FHN)方程的数值解法普遍存在的精度不高、稳定性较弱或算法构造过程较复杂的问题,本文提出了一种将紧致差分格式与保持强稳定龙格库塔法相结合的数值方法。首先,对求解FHN方程所给定的空间区间采用一类六阶紧致差分格式离散,问题简化为求解关于时间的常微分方程组后,再离散时间区间,结合一类改进的四阶显式保持强稳定龙格库塔法,递推求得每一时间层上的解,从而获得了一种简单高效的求解FHN方程的紧致差分算法。将算法运用于两个给定不同初始数据的数值算例,发现算法具有空间六阶精度和较强的稳定性,验证了算法的有效性。
A numerical method that combines compact difference scheme with strong stability preserving Runge-Kutta method is proposed in this paper for solving the common problems of low accuracy,weak stability or complexity of algorithm construction process in the numerical solution of FitzHugh-Nagumo(FHN)equation.Firstly,the givenspace interval is discretized by a class of sixth-order compact difference scheme,and the problem is simplified to be solving the ordinary differential equations about time.Then,the time interval is discretized and the solution at each time level is obtained recursively by a class of modified fourth-order explicit strong-stability-preserving Runge-Kutta method.Thereby,a simple and efficient compact difference algorithm for solving FHN equation is obtained.The algorithm is applied to two numerical exampleswith different giveninitial data,which verifies the effectiveness of the algorithm.It is found that the algorithm is of sixth-order spatial accuracy and strong stability.
作者
张嘉杰
陈豫眉
王小妹
ZHANG Jiajie;CHEN Yumei;WANG Xiaomei(College of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)
出处
《西华师范大学学报（自然科学版）》
2021年第2期126-132,共7页
Journal of China West Normal University(Natural Sciences)
基金
国家自然科学基金面上项目(11971094)
四川省科技厅项目(2017JY0186)
四川省教育厅科研项目重点项目(15ZA0149)。
