Comparative Study of Some Numerical Methods for the Burgers-Huxley Equation

被引：23

作者：

Appadu, Appanah Rao ^{[1
]}

Inan, Bilge ^{[2
]}

Tijani, Yusuf Olatunji ^{[1
]}

机构：

[1] Nelson Mandela Univ, Dept Math & Appl Math, ZA-6031 Port Elizabeth, South Africa

[2] Kilis 7 Aralik Univ, Dept Math, Fac Muallim Rifat Educ, TR-79000 Kilis, Turkey

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 11期

关键词：

Burgers-Huxley equation; nonstandard finite difference method; explicit exponential finite difference method; fully implicit exponential finite difference method; absolute error; relative error; FINITE-DIFFERENCE SCHEME; VARIATIONAL ITERATION METHOD; TRAVELING-WAVE SOLUTIONS; SINGULAR MANIFOLD METHOD; NONCLASSICAL SYMMETRIES; MODELS;

D O I：

10.3390/sym11111333

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we construct four numerical methods to solve the Burgers-Huxley equation with specified initial and boundary conditions. The four methods are two novel versions of nonstandard finite difference schemes (NSFD1 and NSFD2), explicit exponential finite difference method (EEFDM) and fully implicit exponential finite difference method (FIEFDM). These two classes of numerical methods are popular in the mathematical biology community and it is the first time that such a comparison is made between nonstandard and exponential finite difference schemes. Moreover, the use of both nonstandard and exponential finite difference schemes are very new for the Burgers-Huxley equations. We considered eleven different combination for the parameters controlling diffusion, advection and reaction, which give rise to four different regimes. We obtained stability region or condition for positivity. The performances of the four methods are analysed by computing absolute errors, relative errors, L-1 and L-infinity errors and CPU time.

引用

页数：30

共 60 条

[1] Nonstandard finite difference scheme for a Tacoma Narrows Bridge model [J].