A NOTE ON RICHARDSON EXTRAPOLATION OF GALERKIN METHODS FOR EIGENVALUE PROBLEMS OF FREDHOLM INTEGRAL EQUATIONS  

作　　者：Qiumei Huang Yidu Yang 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China [2]School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

出　　处：《Journal of Computational Mathematics》2008年第4期598-612,共15页计算数学（英文）

基　　金：the Governor's Special Foundation of Guizhou Province for Outstanding Scientific Education Personnel (No.[2005]155),China

摘　　要：In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments ave carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.In this paper, we introduce a new extrapolation formula by combining Richardson extrapolation and Sloan iteration algorithms. Using this extrapolation formula, we obtain some asymptotic expansions of the Galerkin finite element method for semi-simple eigenvalue problems of Fredholm integral equations of the second kind and improve the accuracy of the numerical approximations of the corresponding eigenvalues. Some numerical experiments ave carried out to demonstrate the effectiveness of our new method and to confirm our theoretical results.

关 键 词：Fredholm integral equations Semi-simple eigenvalues Asymptotic expansion Galerkin method Richardson extrapolation Sloan iteration. 

分 类 号：O24[理学—计算数学]