Iterated Fast Collocation Methods for Integral Equations of the Second Kind

Authors:
Zhongying Chen;Guangqing Long;Gnaneshwar Nelakanti;Yongdong Zhang
Affiliations:
Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, People's Republic of China 510275;Department of Mathematics, Guangxi Teachers Education University, Nanning, People's Republic of China 530001;Department of Mathematics, Indian Institute of Technology, Kharagpur, India 721302;Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, People's Republic of China 510275
Venue:
Journal of Scientific Computing
Year:
2013

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Abstract

In this paper a new iteration technique is proposed based on fast multiscale collocation methods of Chen et al. (SIAM J Numer Anal 40:344---375, 2002) for Fredholm integral equations of the second kind. It is shown that an additional order of convergence is obtained for each iteration even if the exact solution of the integral equation is non-smooth, the kernel of the integral operator is weakly singular and the matrix compression is implemented. When the solution is smooth, this leads to superconvergence. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.