| 一类脉冲微分方程的渐近解 |
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| 引用本文： | 武利猛,倪明康,陆海波,郑艳.一类脉冲微分方程的渐近解[J].华东师范大学学报(自然科学版),2011,2011(5):60-65. |
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| 作者姓名： | 武利猛 倪明康 陆海波 郑艳 |
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| 作者单位： | 1. 华东师范大学数学系,上海,200241
2. 华东师范大学数学系,上海200241;海高校计算科学E-研究院上海交通大学研究所,上海200240 |
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| 基金项目： | 国家自然科学基金(11071075); 上海市自然科学基金(10ZR1409200); 生物大分子国家重点实验室; 上海市教育委员会E-研究院建设项目(03004) |
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| 摘 要： | 研究一类含有单个脉冲点的脉冲微分方程.基于奇摄动理论,通过分步法,将原脉冲微分方程问题扩充为奇摄动问题,证明了扩充问题的解是原问题解很好的近似,从而为进一步研究脉冲微分方程问题提供了新途径.其次,利用边界层函数法,构造了原问题连续的形式渐近解,证明了解的存在性和进行了余项估计.最后,通过例子验证了主要结果.
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| 关 键 词： | 奇摄动 渐近解 脉冲微分方程 |
| 收稿时间： | 2011-2-1 |
| 修稿时间： | 2011-5-1 |
Asymptotic solution for a class of impulsive differential equations |
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| WU Li-meng,NI Ming-kang,LU Hai-bo,ZHENG Yan.Asymptotic solution for a class of impulsive differential equations[J].Journal of East China Normal University(Natural Science),2011,2011(5):60-65. |
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| Authors: | WU Li-meng NI Ming-kang LU Hai-bo ZHENG Yan |
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| Institution: | 1. Department of Mathematics, East China Normal University, Shanghai 200241, China;
2. Division of Computational Science, E-Institute of Shanghai Universities, SJTU, Shanghai 200240, China |
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| Abstract: | By means of singular perturbation theory, We constructed the singularly perturbed problem for the impulsive differential equation problem, and proved that the solution of the derived problem approximated to the solution of original problem, indicating a new way for the study of impulsive differential equations. By virtue of boundary function method, we not only constructedcontinuous formal asymptotic solution but also proved the existence of solution, meanwhile the remainder estimate was presented. Finally, an example was given to illustrate the results. |
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| Keywords: | singular perturbation asymptotic solution impulsive differential equation |
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