一类Fredholm积分微分方程边值问题的数值方法
Numerical Algorithm for a Class of Fredholm Integro-Differential Boundary Value Problems
DOI: 10.12677/AAM.2017.64075, PDF, HTML, XML, 下载: 1,910  浏览: 3,257  科研立项经费支持
作者: 周永芳, 李景和, 马丽君：河北工业大学理学院，天津；母丽华：黑龙江科技大学理学院，黑龙江 哈尔滨
关键词: 边值问题；积分微分方程；再生核空间；Boundary Value Problems； Integro-Differential Equation； Reproducing Kernel Space
摘要: 本文讨论Fredholm积分微分方程边值问题的数值方法。通过建立满足边界条件的再生核空间，获得简单易行的再生核数值逼近方法。给出方程精确解的级数表达式，通过截断级数获得方程的近似解，并给出了误差估计。数值模拟结果说明本文方法的有效性。
Abstract: This paper discusses the numerical method for a class of Fredholm integro-differential boundary value problems. By constructing the reproducing kernel space which satisfies the boundary condi-tions, the simple reproducing kernel numerical approximate method is established. The paper describes both the exact solution obtained in the form of series and the approximate solution ob-tained by truncating the series representation of the exact solution. Error estimation of the method was discussed. The results of numerical simulation demonstrate the validity of the method in the paper.
文章引用：周永芳, 母丽华, 李景和, 马丽君. 一类Fredholm积分微分方程边值问题的数值方法[J]. 应用数学进展, 2017, 6(4): 644-650. https://doi.org/10.12677/AAM.2017.64075

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