王琦.混合型分段连续微分方程的数值稳定性[J].数学研究及应用,2013,33(1):70~78
混合型分段连续微分方程的数值稳定性
Numerical Stability of Differential Equations with Piecewise Constant Arguments of Mixed Type
投稿时间:2011-04-07  最后修改时间:2012-09-03
DOI:10.3770/j.issn:2095-2651.2013.01.008
中文关键词:  分段连续项  Euler-Maclaurin方法  稳定性.
英文关键词:piecewise constant arguments  Euler-Maclaurin method  stability.
基金项目:国家自然科学基金(Grant No.11201084).
作者单位
王琦 广东工业大学应用数学学院, 广东 广州 510006 
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中文摘要:
      对于混合型分段连续微分方程,分析了Euler-Maclaurin方法的稳定性. 得到了方程解析解的表达式并且给出了解析解的稳定区域,讨论了数值解渐近稳定的充分必要条件,获得了解析解稳定区域包含在数值解稳定区域的条件,并且给出了一些数值例子.
英文摘要:
      This paper deals with the stability analysis of the Euler-Maclaurin method for differential equations with piecewise constant arguments of mixed type. The expression of analytical solution is derived and the stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical examples are given.
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