A highly accurate method to solve Fisher's equation

被引：41

作者：

Bastani, Mehdi ^{[2
]}

Salkuyeh, Davod Khojasteh ^{[1
]}

机构：

[1] Univ Guilan, Fac Math Sci, Rasht, Iran

[2] Univ Mohaghegh Ardabili, Dept Math, Ardebil, Iran

来源：

PRAMANA-JOURNAL OF PHYSICS | 2012年 / 78卷 / 03期

关键词：

Fisher's equation; compact finite difference; Taylor expansion series; total variation diminishing Runge-Kutta; numerical solutions; FINITE-DIFFERENCE SCHEMES; DIFFUSION EQUATION; RUNGE-KUTTA; WAVE; 6TH-ORDER;

D O I：

10.1007/s12043-011-0243-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this study, we present a new and very accurate numerical method to approximate the Fisher's-type equations. Firstly, the spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly, we solve the obtained system of differential equations using a third-order total variation diminishing Runge-Kutta (TVD-RK3) scheme. Numerical examples are given to illustrate the efficiency of the proposed method.

引用

页码：335 / 346

页数：12

共 35 条

[1]

ABLOWITZ MJ, 1979, B MATH BIOL, V41, P835, DOI 10.1007/BF02462380

[2] SOME NUMERICAL EXPERIMENTS ON FISHER EQUATION [J].