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向前型分段连续微分方程的数值解(英文)

Numerical Solutions of Differential Equations with Piecewise Constant Arguments of Advanced Type
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摘要 本文讨论了向前型分段连续微分方程Euler-Maclaurin方法的收敛性和稳定性,给出了Euler-Maclaurin方法的稳定条件,证明了方法的收敛阶是2n+2,并且得到了数值解稳定区域包含解析解稳定区域的条件,最后给出了一些数值例子用以验证本文结论的正确性. This paper is concerned with the convergence and the stability of Euler-Maclaurin methods for solutions of differential equations with piecewise constant arguments of advanced type.The conditions of stability for the Euler-Maclaurin methods are given.It is proved that the order of convergence is 2n＋2.And the conditions under which the numerical stability region contains the analytic stability region are obtained.Finally,several numerical examples are given to demonstrate our main results.
作者 王琦 温洁嫦
机构地区 广东工业大学应用数学学院
出处 《应用数学》 CSCD 北大核心 2011年第4期712-717,共6页 Mathematica Applicata
基金 the National Natural Science Foundation of China(51008084)
关键词 收敛性 稳定性 Euler-Maclaurin方法 分段连续项 Convergence Stability Euler-Maclaurin method Piecewise constant arguments
分类号 O241.81 [理学—计算数学]
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参考文献10

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应用数学
2011年 第4期

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