三阶微分方程边值问题的高效数值算法  

Efficient Numerical Algorithm for Approximate Solution of the Third-Order Differential Equation with Boundary Value Problems

作　　者：牛晶[1] 薛晴[1] 冉翠平 刘佳[1] 潘海静[1] 

机构地区：[1]哈尔滨师范大学数学科学学院,黑龙江哈尔滨150025 [2]哈尔滨师范大学物理与电子工程学院,黑龙江哈尔滨150025

出　　处：《数学的实践与认识》2017年第9期177-181,共5页Mathematics in Practice and Theory

基　　金：黑龙江省教育厅资助项目(12541251)

摘　　要：基于再生核空间法提出了一个高效的数值算法来解决三阶微分方程的边值问题.利用再生性以及正交基的构造,得到了模型精确解的级数表示形式,并通过截断级数获得了其近似解.通过数值算例说明了此方法的有效性.In this paper, we present an efficient numerical algorithm to solve the thirdorder system of boundary value problems based on the reproducing kernel Hilbert space method.Using reproducing property and the existence of orthogonal basis in the reproduc- ing kernel Hilbert space, we obtain a representation of exact solution with form of series and its approximate solution by truncating the series. Moreover, the effectiveness of the presented method is illustrated with two numerical examples.

关 键 词：近似解 再生核空间 数值算法 线性算子 

分 类 号：O175.8[理学—数学]