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Multigrid method for nonlinear integral equations

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Abstract

In this paper, we introduce a multigrid method for solving the nonliear Urysohn integral equation. The algorithm is derived from a discrete resolvent equation which approximates the continuous resolvent equation of the nonlinear Urysohn integral equation. The algorithm is mathematically equivalent to Atkinson’s adaptive twogrid iteration. But the two are different computationally. We show the convergence of the algorithm and its equivalence to Atkinson’s adaptive twogrid iteration. In our numerical example, we compare our algorithm to other multigrid methods for solving the nonliear Urysohn integral equation including the nonlinear multigrid method introduced by Hackbush.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Murray State University, 42071, Murray, KY, USA

    Hosae Lee

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  1. Hosae Lee
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Correspondence to Hosae Lee.

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Lee, H. Multigrid method for nonlinear integral equations. Korean J. Comp. & Appl. Math. 4, 427–440 (1997). https://doi.org/10.1007/BF03014490

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  • DOI: https://doi.org/10.1007/BF03014490

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