Abstract
A simple and efficient method that is called Successive Complementary Expansion Method (SCEM) is applied for approximation to an unstable two-point boundary value problem which is known as Troesch’s problem. In this approach, Troesch’s problem is considered as a singular perturbation problem. We convert the hyperbolic-type nonlinearity into a polynomial-type nonlinearity using an appropriate transformation, and then we use a basic zoom transformation for the boundary layer and finally obtain a nonlinear ordinary differential equation that contains SCEM complementary approximation. We see that SCEM gives highly accurate approximations to the solution of Troesch’s problem for various parameter values. Moreover, the results are compared with Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM) by using tables.
Highlights
Troesch’s highly sensitive problem arises from a system of a nonlinear ordinary differential equations which occur in the investigation of the confinement of a plasma column by radiation pressure [1]
Roberts and Shipman [4] have shown that the closed form solution to problem (1) with the boundary conditions (2) in terms of the Jacobi elliptic function sc(n | m) is as follows: y (x)
The results obtained by Successive Complementary Expansion Method (SCEM) are compared with Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM) and the analytic solutions
Summary
Troesch’s highly sensitive problem arises from a system of a nonlinear ordinary differential equations which occur in the investigation of the confinement of a plasma column by radiation pressure [1]. It arises in the theory of gas porous electrodes [2, 3]. The results obtained by SCEM are compared with HPM and ADM and the analytic solutions
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