A fast multiscale Kantorovich method for weakly singular integral equations

A fast multiscale Kantorovich method for weakly singular integral equations

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Article ID: iaor20132866
Volume: 63
Issue: 1
Start Page Number: 49
End Page Number: 63
Publication Date: May 2013
Journal: Numerical Algorithms
Authors: , ,
Keywords: integration
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.

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