Successive Complementary Expansion Method for Solving Troesch’s Problem as a Singular Perturbation Problem
| Autor: | Süleyman Cengizci, Aytekin Eryılmaz |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Singular perturbation
Article Subject lcsh:Mathematics Mathematical analysis lcsh:QA1-939 Nonlinear system Boundary layer Transformation (function) Simple (abstract algebra) lcsh:TA1-2040 Boundary value problem Zoom lcsh:Engineering (General). Civil engineering (General) Adomian decomposition method Mathematics |
| Zdroj: | International Journal of Engineering Mathematics, Vol 2015 (2015) |
| ISSN: | 2314-6109 2356-7007 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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