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.