利用再生核解一类常微分方程  

Solving a class of ordinary differential equation using reproducing kernel

作　　者：王玉兰[1] 苏丽娟[1] 朝鲁[1,2] 

机构地区：[1]内蒙古工业大学数学系,呼和浩特010051 [2]上海海事大学应用数学物理所,上海200135

出　　处：《黑龙江大学自然科学学报》2009年第2期150-153,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10461005);内蒙古工业大学重点基金资助项目(ZD200709)

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。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 also possessing good accuracy.

关 键 词：常微分方程 再生核 迭代方法 

分 类 号：O175.1[理学—数学]