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Numerical Verification of Solutions of Periodic Integral Equations with a Singular Kernel

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Abstract

This paper proposes the method of numerical verification of solutions of a periodic integral equation with a logarithmic singular kernel, which is typically found in some two-dimensional potential problems. The verification method utilizes a property of the singular integral for trigonometric polynomials, the periodic Sobolev space and Schauder's fixed point theorem.

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References

  1. H.-J. Dobner, Verification methods for Fredholm integral equations, Internat. J. Comput. Math. 48, 251–261.

  2. R. Kress, Linear Integral Equations (Springer, Berlin, 1999).

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Authors and Affiliations

  1. Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan

    Sunao Murashige

  2. Department of Computer and Information Science, School of Science and Engineering, Waseda University, Tokyo, 169-855, Japan

    Shin'ichi Oishi

Authors
  1. Sunao Murashige
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  2. Shin'ichi Oishi
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Murashige, S., Oishi, S. Numerical Verification of Solutions of Periodic Integral Equations with a Singular Kernel. Numerical Algorithms 37, 301–310 (2004). https://doi.org/10.1023/B:NUMA.0000049476.37729.99

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  • DOI: https://doi.org/10.1023/B:NUMA.0000049476.37729.99

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