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Scott, M (1975) On the Conversion of Boundary-Value Problems into Stable Initial Value Problems via Several Invariant Imbedding Algorithms. In: Aziz, A.K., Ed., Numerical Solution of Boundary-Value Problems for Ordinary Differential Equations.

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• TITLE: A Logarithmic Finite Difference Method for Troesch’s Problem

  AUTHORS: M. S. Ismail, K. S. Al-Basyoni

  KEYWORDS: Troesch’s Problem, Logarithmic Finite Difference Method, Inverse Sine Hyperbolic

  JOURNAL NAME: Applied Mathematics, Vol.9 No.5, May 30, 2018

  ABSTRACT: The aim of this paper is to derive a numerical scheme for Troesch’s problem and to overcome the difficulty which faces the existing numerical methods when considering the Troesch’s problem with large values of λ. A logarithmic finite difference method is derived for solving the Troesch’s problem. The method is very simple and works well for arbitrarily large values of the Troesch’s parameter. To test the proposed method, we have used a wide range of the Troesch’s parameter λ. A comparison with some existing methods is given. The numerical results show the robustness and the superiority of the proposed scheme over most of the existing numerical methods for the Troesch’s problem.