Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

被引：30
作者：
Liang, Hui [1 ]
Shi, Dongyang [2 ]
Lv, Wanjin [1 ]
机构：
[1] Heilongjiang Univ, Sch Math Sci, Harbin 150080, Peoples R China
[2] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 02期
关键词：
Galerkin methods; Convergence; Asymptotic stability; Piecewise constant arguments; Partial differential equation; RUNGE-KUTTA METHODS; NUMERICAL-SOLUTION; AU(T) PLUS; U'(T);
D O I：
10.1016/j.amc.2010.06.028
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper deals with the convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument. The optimal convergence orders are obtained for the semidiscrete and full discrete (backward Euler) methods respectively. Both the discrete solutions are proved to be asymptotically stable under the condition that the analytical solution is asymptotically stable. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：854 / 860
页数：7
相关论文
共 12 条
[1]  
COOKE KL, 1984, J MATH ANAL APPL, V99, P256
[2]   Stability of θ-schemes in the numerical solution of a partial differential equation with piecewise continuous arguments [J].
Liang, Hui ;
Liu, M. Z. ;
Lv, Wanjin .
APPLIED MATHEMATICS LETTERS, 2010, 23 (02) :198-206
[3]   Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments [J].
Liu, M. Z. ;
Ma, S. F. ;
Yang, Z. W. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (01) :57-66
[4]   Stability of Runge-Kutta methods in the numerical solution of equation u′(t) = au(t) plus a0u([t]) [J].
Liu, MZ ;
Song, MH ;
Yang, ZW .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 166 (02) :361-370
[5]  
Shah S. M., 1983, Int. J. Math. Math. Sci, V6, P671, DOI [10.1155/S0161171283000599, DOI 10.1155/S0161171283000599]
[6]   Stability of θ-methods for advanced differential equations with piecewise continuous arguments [J].
Song, MH ;
Yang, ZW ;
Liu, MZ .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (9-10) :1295-1301
[7]  
Thomee V., 1997, GALERKIN FINITE ELEM
[8]  
Wiener J, 1993, GEN SOLUTIONS DIFFER
[9]  
Wiener J., 1983, TRENDS THEORY PRACTI
[10]  
Wiener J., 1991, Int. J. Comput. Math, V14, P363, DOI DOI 10.1155/S0161171291000431
12