Numerical methods for the generalized Fisher-Kolmogorov-Petrovskii-Piskunov equation

被引：55
作者：
Branco, J. R.
Ferreira, J. A.
de Oliveira, P.
机构：
[1] Univ Coimbra, Dept Matemat, P-3001454 Coimbra, Portugal
[2] Inst Super Engn Coimbra, Dept Fis Matemat, P-3030199 Coimbra, Portugal
来源：
APPLIED NUMERICAL MATHEMATICS | 2007年 / 57卷 / 01期
关键词：
Fisher equation; integro-differentiall equation; numerical approximation; stability;
D O I：
10.1016/j.apnum.2006.01.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study numerical methods for solving integro-differential equations which generalize the well-known Fisher equation. The numerical methods are obtained considering the MOL (Method of Lines) approach. The stability and convergence of the methods are studied. Numerical results illustrating the theoretical results proved are also included. (c) 2006 IMACS. Published by Elsevier B.V. All rights reserved.
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页码：89 / 102
页数：14
相关论文
共 10 条
[1]  
[Anonymous], 1962, NUMER MATH
[2]   MULTIDIMENSIONAL NON-LINEAR DIFFUSION ARISING IN POPULATION-GENETICS [J].
ARONSON, DG ;
WEINBERGER, HF .
ADVANCES IN MATHEMATICS, 1978, 30 (01) :33-76
[3]   Nonuniform reaction rate distribution for the generalized Fisher equation: Ignition ahead of the reaction front [J].
Fedotov, S .
PHYSICAL REVIEW E, 1999, 60 (04) :4958-4961
[4]   Traveling waves in a reaction-diffusion system: Diffusion with finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics [J].
Fedotov, S .
PHYSICAL REVIEW E, 1998, 58 (04) :5143-5145
[5]   Front propagation into an unstable state of reaction-transport systems [J].
Fedotov, S .
PHYSICAL REVIEW LETTERS, 2001, 86 (05) :926-929
[6]   Hyperbolic reaction-diffusion equations for a forest fire model [J].
Mendez, V ;
Llebot, JE .
PHYSICAL REVIEW E, 1997, 56 (06) :6557-6563
[7]   Dynamics and thermodynamics of delayed population growth [J].
Mendez, V ;
Camacho, J .
PHYSICAL REVIEW E, 1997, 55 (06) :6476-6482
[8]  
Mendez V., 2002, PHYS REV E, V65, P1
[9]   TIME DISCRETIZATION OF AN INTEGRODIFFERENTIAL EQUATION OF PARABOLIC TYPE [J].
SLOAN, IH ;
THOMEE, V .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1986, 23 (05) :1052-1061
[10]  
ZHANG NY, 1993, MATH COMPUT, V60, P133, DOI 10.1090/S0025-5718-1993-1149295-4
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