再生核结合配置法求解一类带有积分边值条件的四阶非线性微分方程

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 928-936.

再生核结合配置法求解一类带有积分边值条件的四阶非线性微分方程

刘宏影, 吕学琴

哈尔滨师范大学数学科学学院哈尔滨 150025

收稿日期:2015-12-05 修回日期:2016-04-26 出版日期:2016-10-26 发布日期:2016-10-26
通讯作者: 吕学琴,E-mail:hashidalvxueqin@126.com E-mail:hashidalvxueqin@126.com
作者简介:吕学琴,E-mail:hashidalvxueqin@126.com
基金资助:
国家自然科学基金（11401145）、黑龙江省教育厅项目（12531180）和黑龙江省青年基金项目（JJ2016QN0211）资助

Method for Solving a Class of Fourth Order Nonlinear Differential Equations with Integral Boundary Conditions by Combining Collocation Method and Reproducing Kernel Method

Liu Hongying, Lv Xueqin

School of Mathematics and Sciences, Harbin Normal University, Harbin 150025

Received:2015-12-05 Revised:2016-04-26 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11401145), the Educational Department Scientific Technology Program of Heilongjiang Province (12531180) and the Youth Foundation of Heilongjiang Province (JJ2016QN0211)

摘要/Abstract

摘要：

该文主要研究了一类带有积分边值条件的四阶非线性微分方程的求解.利用再生核理论结合配置法来求解此类问题，并着重说明了用此种方法得到的解的一致收敛性.同时给出了算例说明了该方法的有效性.

关键词: 配置法, 积分边值条件, 四阶非线性微分方程, 再生核空间

Abstract:

In this paper, we study to solve a class of fourth order nonlinear differential equations with integral boundary conditions by combining collocation method and reproducing kernel method and especially illustrates the uniform convergence of the solution obtained by this method. Some numerical examples are displayed to demonstrate the validity and applicability of the present method.

Key words: Collocation method, Integral boundary conditions, Fourth order nonlinear differential equations, Reproducing kernel space

中图分类号:

O241.5

刘宏影, 吕学琴. 再生核结合配置法求解一类带有积分边值条件的四阶非线性微分方程[J]. 数学物理学报, 2016, 36(5): 928-936.

Liu Hongying, Lv Xueqin. Method for Solving a Class of Fourth Order Nonlinear Differential Equations with Integral Boundary Conditions by Combining Collocation Method and Reproducing Kernel Method[J]. Acta mathematica scientia,Series A, 2016, 36(5): 928-936.

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