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

作　　者：周永芳 母丽华 李景和[1] 马丽君 

机构地区：[1]河北工业大学理学院,天津 [2]黑龙江科技大学理学院,黑龙江哈尔滨

出　　处：《应用数学进展》2017年第4期644-650,共7页Advances in Applied Mathematics

基　　金：河北省自然科学基金(A2015202335);黑龙江省自然科学基金(A201421)。

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。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.

关 键 词：边值问题 积分微分方程 再生核空间 

分 类 号：O1[理学—数学]