Oscillation analysis of numerical solution in the θ-methods for equation x′(t)+ax(t)+a1x([t-1])=0

被引：27
作者：
Liu, M. Z. [1 ]
Gao, Jianfang [1 ]
Yang, Z. W. [1 ]
机构：
[1] Harbin Inst Technol, Dept Math, Harbin 150001, Heilongjiang, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 186卷 / 01期
关键词：
numerical solution; delay differential equation; oscillation; linear interpolation;
D O I：
10.1016/j.amc.2006.07.119
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The paper deals with the oscillation analysis of numerical solution in the theta-methods for equation x'(t) + ax(t) + a(1)x([t - 1]) = 0. The conditions of the oscillation for the theta-method are obtained. It is proved that the oscillation of the analytic solution is preserved by the theta-method. It turns out that the zeros of the linear interpolation function of the numerical solution can converge to the zeros of the analytic solution with the order of accuracy 1 (theta not equal 1/2) and 2 (theta = 1/2). Some numerical experiments are given. (c) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码：566 / 578
页数：13
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