Numerical solution of the one-dimensional Burgers' equation: Implicit and fully implicit exponential finite difference methods

被引：39
|
作者：
Inan, Bilge [1 ]
Bahadir, Ahmet Refik [1 ]
机构：
[1] Inonu Univ, Fac Arts & Sci, Dept Math, TR-44280 Malatya, Turkey
来源：
PRAMANA-JOURNAL OF PHYSICS | 2013年 / 81卷 / 04期
关键词：
Burgers' equation; exponential finite difference method; implicit exponential finite difference method; fully implicit exponential finite difference method; SCHEME; EXPLICIT;
D O I：
10.1007/s12043-013-0599-z
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
This paper describes two new techniques which give improved exponential finite difference solutions of Burgers' equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers' equation. As the Burgers' equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton's method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.
引用
收藏
页码：547 / 556
页数：10
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