关于边值问题的一种新的再生核数值算法  

A New Reproducing Kernel Method for Boundary Value Problems

作　　者：朱慧[1] 林迎珍[1] 

机构地区：[1]北京理工大学珠海学院数理与土木工程学院

出　　处：《数学的实践与认识》2015年第23期249-254,共6页Mathematics in Practice and Theory

摘　　要：利用一种新的再生核算法讨论了二阶微分方程边值问题的数值解,并证明了解的收敛性.算法中,定义了再生核空间,避开了施密特正交化过程,借助于逆矩阵给出了近似解的表达式.通过数值算例,分析了数值解的逼近效果,并与泰勒级数法进行了比较,说明了方法的实用性和有效性.In this paper, a new reproducing kernel method is presented for numerically solving second order boundary value problems. And the convergence of the numerical solution is proved. In the algorithm, we define the reproducing kernel space and give the approximate solution by using inverse matrix. The Schmidt orthogonalization process is avoided. An numerical example is studied to show that a good approximation is obtained. Moreover, compared with the Taylor expansion method, the new reproducing kernel method is more practical and effective.

关 键 词：边值问题 再生核 数值算法 

分 类 号：O241.8[理学—计算数学]