A fast multiscale Kantorovich method for weakly singular integral equations

Authors:
Guangqing Long;Weifen Wu;Gnaneshwar Nelakanti
Affiliations:
Department of Mathematics, Guangxi Normal College, Nanning, People's Republic of China 530001;Department of Mathematics, Guangxi Normal College, Nanning, People's Republic of China 530001;Department of Mathematics, Indian Institute of Technology, Kharagpur, India 721302
Venue:
Numerical Algorithms
Year:
2013

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Abstract

In this paper, we use the idea of Kantorovich regularization to develop the fast multiscale Kantorovich method and the fast iterated multiscale Kantorovich method. For some kinds of weakly singular integral equations with nonsmooth inhomogeneous terms, we show that our two proposed methods can still obtain the optimal order of convergence and superconvergence order, respectively. Numerical examples are given to demonstrate the efficiency of the methods.