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Singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel

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Abstract

In a recent paper [3], Cao and Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend the result of Cao and Xu and to establish the singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. The iterated singularity preserving Galerkin method is also discussed.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529-0077, USA

    Hideaki Kaneko & Richard D. Noren

  2. NASA Langley Research Center, MS-130, Hampton, VA, 23681-0001, USA

    Peter A. Padilla

Authors
  1. Hideaki Kaneko
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  2. Richard D. Noren
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  3. Peter A. Padilla
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Kaneko, H., Noren, R.D. & Padilla, P.A. Singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. Advances in Computational Mathematics 9, 363–376 (1998). https://doi.org/10.1023/A:1018910128100

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