Fourth-order finite difference method for solving Burgers' equation

被引：115
作者：
Hassanien, IA
Salama, AA [1 ]
Hosham, HA
机构：
[1] Assiut Univ, Fac Sci, Dept Math, Assiut 71516, Egypt
[2] Al Azhar Univ, Fac Sci, Dept Math, Assiut 71524, Egypt
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2005年 / 170卷 / 02期
关键词：
Burgers' equation; finite difference method; stability; convergence;
D O I：
10.1016/j.amc.2004.12.052
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we present fourth-order finite difference method for solving nonlinear one-dimensional Burgers' equation. This method is unconditionally stable. The convergence analysis of the present method is studied and an upper bound for the error is derived. Numerical comparisons are made with most of the existing numerical methods for solving this equation. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：781 / 800
页数：20
相关论文
共 26 条
[1]   A numerical solution of Burgers' equation [J].
Aksan, EN ;
Özdes, A .
APPLIED MATHEMATICS AND COMPUTATION, 2004, 156 (02) :395-402
[2]   A COLLOCATION SOLUTION FOR BURGERS-EQUATION USING CUBIC B-SPLINE FINITE-ELEMENTS [J].
ALI, AHA ;
GARDNER, GA ;
GARDNER, LRT .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1992, 100 (03) :325-337
[3]  
[Anonymous], 1992, NUMER METHODS PARTIA, DOI DOI 10.1002/NUM.1690080303
[4]  
[Anonymous], 1965, Nonlinear partial differential equations in engineering
[5]  
Bateman H., 1915, Mon. Weather Rev., V43, P163
[6]   TABLE OF SOLUTIONS OF ONE-DIMENSIONAL BURGERS EQUATION [J].
BENTON, ER ;
PLATZMAN, GW .
QUARTERLY OF APPLIED MATHEMATICS, 1972, 30 (02) :195-&
[7]  
BERGER AE, 1980, MATH COMPUT, V35, P695, DOI 10.1090/S0025-5718-1980-0572850-8
[8]  
Burgers J., 1948, Adv. Appl. Mech., DOI 10.1016/S0065-2156(08)70100-5
[9]  
Burgers J M., 1939, T ROY NETH ACAD SCI, V17, P1
[10]   SOLUTION OF BURGERS-EQUATION FOR LARGE REYNOLDS-NUMBER USING FINITE-ELEMENTS WITH MOVING NODES [J].
CALDWELL, J ;
WANLESS, P ;
COOK, AE .
APPLIED MATHEMATICAL MODELLING, 1987, 11 (03) :211-214
123