| 利用再生核解一类常微分方程 |
| |
| 引用本文： | 王玉兰,苏丽娟,朝鲁. 利用再生核解一类常微分方程[J]. 黑龙江大学自然科学学报, 2009, 26(2) |
| |
| 作者姓名： | 王玉兰 苏丽娟 朝鲁 |
| |
| 作者单位： | 内蒙古工业大学,数学系,呼和浩特,010051;内蒙古工业大学,数学系,呼和浩特,010051;上海海事大学,应用数学物理所,上海,200135 |
| |
| 基金项目： | 国家自然科学基金，内蒙古工业大学重点基金 |
| |
| 摘 要： | 充分运用再生核的技巧,给出了一类常微分方程边值问题的精确解的级数形式表达式,为了得到边值问题的近似解,描述了迭代解法并进行了理论分析.本方法的优点在于构造了新基底,绕过了求施密特正交化的麻烦.通过数值例子验证了该方法不仅有效而且高精度.
|
| 关 键 词： | 常微分方程 再生核 迭代方法 |
Solving a class of ordinary differential equation using reproducing kernel |
| |
| WANG Yu-lan,SU Li-juan,CHAO Lu. Solving a class of ordinary differential equation using reproducing kernel[J]. Journal of Natural Science of Heilongjiang University, 2009, 26(2) |
| |
| Authors: | WANG Yu-lan SU Li-juan CHAO Lu |
| |
| Affiliation: | 1. Department of Mathematics;Inner Mongolia University of Technology;Hohhot 010051;China;2. Institute of Applied Mathematics and Pgysics of Shanghai Maritime University;Shanghai 200315;China |
| |
| Abstract: | A series representation of exact solutions of a class of boundary value problems of ordinary differential equations is given by making good use of reproducing kernel techniques. For getting the approximate solution,A iterative method is presented and its theoretical analysis is done. The advantage of the method lies in employing a new basic function and avoiding to the Schmidt orthogonalization. Results of some numerical examples have demonstrated that the proposed approach is not only effectiveness but als... |
| |
| Keywords: | ordinary differential equation reproducing kernel iterative method |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
