Successive Complementary Expansion Method for Solving Troesch’s Problem as a Singular Perturbation Problem

A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied forapproximation to an unstable two-point boundary value problem which is knownas Troesch’s problem. In this approach, Troesch’s problem is considered as asingular perturbation problem. We convert the hyperbolic-type nonlinearityinto a polynomial-type nonlinearity using an appropriate transformation, andthen we use a basic zoom transformation for the boundary layer and finallyobtain a nonlinear ordinary differential equation that contains SCEMcomplementary approximation. We see that SCEM gives highly accurateapproximations to the solution of Troesch’s problem for various parametervalues. Moreover, the results are compared with Adomian Decomposition Method (ADM)and Homotopy Perturbation Method (HPM) by using tables