SUPERGEOMETRIC CONVERGENCE OF SPECTRAL COLLOCATION METHODS FOR WEAKLY SINGULAR VOLTERRA AND FREDHOLM INTEGRAL EQUATIONS WITH SMOOTH SOLUTIONS  

作　　者：Can Huang Tao Tang Zhimin Zhang 

机构地区：[1]Department of Mathematics, Wayne State University, Detroit, MI 48202, USA [2]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong [3]Department of Mathematics, Wayne State University, MI 48202, USA

出　　处：《Journal of Computational Mathematics》2011年第6期698-719,共22页计算数学（英文）

基　　金：This research is partially supported by the GRF grants of Hong Kong Research Grant Council; the FRG grants of Hong Kong Baptist University; the US National Science Foundation through grant DMS-0612908; the Ministry of Education of China through the Changjiang Scholars program; and Guangdong Provincial Government of China through the ＂Computational Science Innovative Research Team＂ program.

摘　　要：A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.

关 键 词：Weakly singular kernel Integro-differential equations Collocation method. 

分 类 号：O241.83[理学—计算数学] O175.6[理学—数学]