非线性 Fredholm 积分方程迭代 Galerkin 解的渐近展开及其外推  

ASYMPTOTIC ERROR EXPANSION AND EXTRAPOLATION FOR THE ITERATED GALERKIN SOLUTION OF NONLINEAR FREDHOLM INTEGRAL EQUATION

作　　者：韩国强[1] 林伟健[1] 

机构地区：[1]华南理工大学计算机工程与科学系

出　　处：《华南理工大学学报（自然科学版）》1997年第6期119-126,共8页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金;广东省自然科学基金

摘　　要：讨论了一维非线性Ｆｒｅｄｈｏｌｍ积分方程迭代Ｇａｌｅｒｋｉｎ方法，证明了迭代Ｇａｌｅｒｋｉｎ解的误差可展开为ｈ的偶次幂，且首项为ｈ２ｐ。从而可进行Ｒｉｃｈａｒｄｓｏｎ外推，提高数值解的精度。同时我们还给出了数值例子，数值计算结果与理论预测相符。This paper discusses the asymptotic error expansion of the iterated Galerkin solution for one dimensional nonlinear Fredholm integral equation of the second kind.It proves that the iterated Galerkin solution admits an error expansion in even powers of the step sized h ,beginning with a term h .Thus Richardson's extrapolation can be performed on the solution,and this will greatly increase the accuracy of the numerical solution.Some numerical results are given in the paper.

关 键 词：FREDHOLM积分方程 迭代Galerkin方法 渐近展开 RICHARDSON外推 

分 类 号：O241.83[理学—计算数学] O175[理学—数学]