AN IMPROVED SECOND-ORDER NUMERICAL METHOD FOR THE GENERALIZED BURGERS-FISHER EQUATION

被引：6
作者：
Bratsos, A. G. [1 ]
机构：
[1] Technol Educ Inst TEI Athens, Dept Math, Athens 12210, Greece
来源：
ANZIAM JOURNAL | 2013年 / 54卷 / 03期
关键词：
generalized Burgers-Fisher equation; reaction-diffusion equation; finite-difference method; bistable medium; travelling kink waves; modified predictor-corrector method; TANH-COTH METHOD; EXPLICIT SOLUTIONS; SCHEME; HUXLEY; FORMS;
D O I：
10.1017/S1446181113000138
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A second-order in time finite-difference scheme using a modified predictor-corrector method is proposed for the numerical solution of the generalized Burgers-Fisher equation. The method introduced, which, in contrast to the classical predictor-corrector method is direct and uses updated values for the evaluation of the components of the unknown vector, is also analysed for stability. Its efficiency is tested for a single-kink wave by comparing experimental results with others selected from the available literature. Moreover, comparisons with the classical method and relevant analogous modified methods are given. Finally, the behaviour and physical meaning of the two-kink wave arising from the collision of two single-kink waves are examined.
引用
收藏
页码：181 / 199
页数：19
相关论文
共 31 条
[1]  
ABLOWITZ MJ, 1979, B MATH BIOL, V41, P835, DOI 10.1007/BF02462380
[2]  
[Anonymous], 1937, Bull. Univ. Mosc. Ser. Int. A, DOI DOI 10.1016/B978-0-08-092523-3.50014-9
[3]   Analytic approximate solutions to Burgers, Fisher, Huxley equations and two combined forms of these equations [J].
Babolian, E. ;
Saeidian, J. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (05) :1984-1992
[4]   A numerical method for the one-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2008, 24 (03) :833-844
[5]   A modified explicit numerical scheme for the two-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2008, 85 (02) :241-252
[6]   A third order numerical scheme for the two-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2007, 76 (04) :271-282
[7]   A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation [J].
Bratsos, A. G. .
NUMERICAL ALGORITHMS, 2006, 43 (04) :295-308
[8]   A fourth-order numerical scheme for solving the modified Burgers equation [J].
Bratsos, A. G. .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (05) :1393-1400
[9]   A second order numerical scheme for the solution of the one-dimensional Boussinesq equation [J].
Bratsos, Athanassios G. .
NUMERICAL ALGORITHMS, 2007, 46 (01) :45-58
[10]  
Brazhnik P. K., 1999, SIAM Journal on Applied Mathematics, V60, P371
1234