| 向前型分段连续微分方程的数值解 |
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| 引用本文： | 王琦,温洁嫦. 向前型分段连续微分方程的数值解[J]. 应用数学, 2011, 24(4): 712-717 |
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| 作者姓名： | 王琦 温洁嫦 |
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| 作者单位： | 广东工业大学应用数学学院,广东广州,510006 |
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| 基金项目： | the National Natural Science Foundation of China(51008084) |
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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.
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| 关 键 词： | 收敛性 稳定性 Euler-Maclaurin方法 分段连续项 |
Numerical Solutions of Differential Equations with Piecewise Constant Arguments of Advanced Type |
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| WANG Qi , WEN Jiechang. Numerical Solutions of Differential Equations with Piecewise Constant Arguments of Advanced Type[J]. Mathematica Applicata, 2011, 24(4): 712-717 |
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| Authors: | WANG Qi WEN Jiechang |
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| Affiliation: | WANG Qi,WEN Jiechang (Faculty of Apllied Mathematics,Guangdong University of Technology,Guangzhou 510006,China) |
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| Abstract: | 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. |
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| Keywords: | Convergence Stability Euler-Maclaurin method Piecewise constant arguments |
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