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A fast multiscale Kantorovich method for weakly singular integral equations

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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.

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Authors and Affiliations

  1. Department of Mathematics, Guangxi Normal College, Nanning, 530001, People’s Republic of China

    Guangqing Long & Weifen Wu

  2. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India

    Gnaneshwar Nelakanti

Authors
  1. Guangqing Long
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  2. Weifen Wu
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  3. Gnaneshwar Nelakanti
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Correspondence to Guangqing Long.

Additional information

Supported in part by Natural Science Foundation of China under grant 11061008 and 10901093, the NSF of Guangxi Province under grant 2011GXNSFA018128 and Program for Excellent Talents in Guangxi Higher Education Institutions.

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Long, G., Wu, W. & Nelakanti, G. A fast multiscale Kantorovich method for weakly singular integral equations. Numer Algor 63, 49–63 (2013). https://doi.org/10.1007/s11075-012-9610-x

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  • DOI: https://doi.org/10.1007/s11075-012-9610-x

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