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| 奇异摄动滞时微分方程的一致收敛数值方法 | |
| 引用本文： | 孙业国,张东月,田红炯.奇异摄动滞时微分方程的一致收敛数值方法[J].系统仿真学报,2007,19(17):3943-3944,3992. |
| 作者姓名： | 孙业国 张东月 田红炯 |
| 作者单位： | 1. 上海师范大学数学系,上海,200234;淮南师范学院数学系,安徽,232001 2. 上海师范大学数学系,上海,200234 3. 上海师范大学数学系,上海,200234;上海高校计算科学E-研究院,上海,200234 |
| 基金项目： | 国家自然科学基金;上海市教委资助项目;上海市科委资助项目;上海市自然科学基金 |
| 摘 要： | 提出了求解线性奇异摄动滞时微分方程基于指数拟合技术的一致收敛和最佳一致收敛的数值方法，并证明了方法的一致收敛性。利用线性化的思想，并结合Newton-Raphson迭代，构造了求解非线性奇异摄动滞时微分方程相应的一致收敛的算法．数值例子验证上述理论结论的正确性。 |
| 关 键 词： | 奇异摄动 滞时微分方程 一致收敛 数值方法 |
| 文章编号： | 1004-731X（2007）17-3943-02 |
| 收稿时间： | 2006-09-10 |
| 修稿时间： | 2006-09-102007-03-15 |
Uniformly Convergent Numerical Methods for Singularly Perturbed Delay Differential Equations |
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| SUN Ye-guo,ZHANG Dong-yue,TIAN Hong-jiong.Uniformly Convergent Numerical Methods for Singularly Perturbed Delay Differential Equations[J].Journal of System Simulation,2007,19(17):3943-3944,3992. | |
| Authors: | SUN Ye-guo ZHANG Dong-yue TIAN Hong-jiong |
| Institution: | 1. Department of Mathematics, Shanghai Normal University, Shanghai 200234, China; 2. Division of Computational Science, E-Institute of Shanghai Universities, Shanghai 200234, China 3. Department of Mathematics, Huainan Normal University, Anhui 232001, China |
| Abstract: | Uniformly convergent and optimal uniformly convergent numerical schemes based on the exponential fitting technique were proposed for solving linear singular perturbation problems with afterffect. Corresponding uniformly convergent numerical schemes were constructed by linearization combined with Newton-Raphson iteration for nonlinear problems. Numerical examples were given to confirm the theoretical results. |
| Keywords: | singular perturbation delay differential equation uniform convergence numerical method |
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