Solving singular perturbation with one boundary layer problem of second order ODE using the method of matched asymptotic expansion (MMAE) / Firdawati Mohamed and Masnira Ramli

Mohamed, Firdawati and Ramli, Masnira (2018) Solving singular perturbation with one boundary layer problem of second order ODE using the method of matched asymptotic expansion (MMAE) / Firdawati Mohamed and Masnira Ramli. Journal of Mathematics and Computating Science, 1 (1). pp. 9-18. ISSN 0128-0767

Abstract

Any physical problems when modeled into equations, may become linear or nonlinear equations with known and unknown boundaries. The exact solution for those equations is not easy to obtain. Hence, an analytical approximation solution in terms of asymptotic expansion is sought. This study seeks to solve a singular perturbation in second order ordinary differential equations. Solutions to several perturbed ordinary differential equations are obtained in terms of asymptotic expansion. The main focus of this study is to find an approximate analytical solution for perturbation problems (linear and nonlinear equations) that occur at one boundary layer using the classical method of matched asymptotic expansion (MMAE). Besides, the underlying concepts and principles of MMAE will also be clarified. Mathematica computer algebra system is used to perform the detail algebraic computations. The results of approximation analytical solution are illustrated by graphs using selected parameters which show the outer, inner and composite solutions separately. Hence, the exact solution and composite solution obtained using MMAE are compared by plotting the graph to show their accuracy. From the comparison, MMAE is one of the best methods to solve singular perturbation problems in second order ordinary differential equation since the results obtained are very close to the exact solution.

Metadata

Item Type: Article
Creators:
CreatorsID Num. / Email
Mohamed, Firdawatifirdawati02@kelantan.uitm.edu.my
Ramli, Masniramasnira@kelantan.uitm.edu.my
Subjects: Q Science > QA Mathematics > Analysis
Divisions: Universiti Teknologi MARA, Kelantan > Machang Campus > Faculty of Computer & Mathematical Sciences
Journal or Publication Title: Journal of Mathematics and Computating Science
Journal: UiTM Journal > Journal of Mathematics and Computing Science
ISSN: 0128-0767
Volume: 1
Number: 1
Page Range: pp. 9-18
Official URL: http://jmcs.com.my/index.php/jmcs/article/view/2
Item ID: 24204
Uncontrolled Keywords: MMAE, Outer Solution, Inner Solution, Composite Solution
URI: http://ir.uitm.edu.my/id/eprint/24204

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