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A Logarithmic Finite Difference Method for Troesch’s Problem

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Document pages: 10 pages

Abstract: The aim of this paper is to derive a numerical scheme for Troesch’s problemand to overcome the difficulty which faces the existing numerical methodswhen considering the Troesch’s problem with large values of λ. A logarithmicfinite difference method is derived for solving the Troesch’s problem. Themethod is very simple and works well for arbitrarily large values of theTroesch’s parameter. To test the proposed method, we have used a wide rangeof the Troesch’s parameter λ. A comparison with some existing methods isgiven. The numerical results show the robustness and the superiority of theproposed scheme over most of the existing numerical methods for theTroesch’s problem.

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