INVESTIGATION OF APPROXIMATE SOLUTION OF MATHEMATICAL MODEL OF SINGULAR PERTURBATION PROBLEM OF INCLUDING SECOND ORDER LINEAR EQUATION WITH VARIABLE COEFFICIENTS AND DIRICHLET BOUNDARY CONDITIONS

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SARAKHSI ALI REZA; JAHANSHAHI MOHAMMAD; SARAKHSI MOJTABA

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2013 | Volume:2 | Issue:2 Page(s): 49-70

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Title

INVESTIGATION OF APPROXIMATE SOLUTION OF MATHEMATICAL MODEL OF SINGULAR PERTURBATION PROBLEM OF INCLUDING SECOND ORDER LINEAR EQUATION WITH VARIABLE COEFFICIENTS AND DIRICHLET BOUNDARY CONDITIONS

Author(s)

SARAKHSI ALI REZA | JAHANSHAHI MOHAMMAD | SARAKHSI MOJTABA | Issue Writer Certificate

Keywords

BOUNDARY LAYER PROBLEMQ3

ASYMPTOTIC EXPANSION OF SOLUTIONQ3

MATCHING CONDITIONSQ3

Abstract

The main subject of this paper is to consider the solution of singular perturbation problems which these problems appear in physical and engineering problems, such as fluid mechanics, chemical reactions, electronic circuitry, civil and fluid dynamics. In fact, a singular perturbation problem is in the form of either ordinary differential equations (O.D.E) or partial differential equations (P.D.E) in which the highest derivative is multiplied by some powers of as a positive small parameter. The purpose of the theory of singular perturbations is to solve a differential equation with some initial or boundary conditions with a small parameter. In this paper, the structure of solutions of these problems for second order ordinary differential equations with variable coefficients is considered. The next goal of this paper is to verify formation and non-formation of boundary layers in boundary points. Finally, the asymptotic expansions and uniform approximate solutions are obtained in five steps by using asymptotic matching condition.

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APA: Copy

SARAKHSI, ALI REZA, JAHANSHAHI, MOHAMMAD, & SARAKHSI, MOJTABA. (2013). INVESTIGATION OF APPROXIMATE SOLUTION OF MATHEMATICAL MODEL OF SINGULAR PERTURBATION PROBLEM OF INCLUDING SECOND ORDER LINEAR EQUATION WITH VARIABLE COEFFICIENTS AND DIRICHLET BOUNDARY CONDITIONS. ADVANCES IN MATHEMATICAL MODELING, 2(2), 49-70. SID. https://sid.ir/paper/243888/en

Vancouver: Copy

SARAKHSI ALI REZA, JAHANSHAHI MOHAMMAD, SARAKHSI MOJTABA. INVESTIGATION OF APPROXIMATE SOLUTION OF MATHEMATICAL MODEL OF SINGULAR PERTURBATION PROBLEM OF INCLUDING SECOND ORDER LINEAR EQUATION WITH VARIABLE COEFFICIENTS AND DIRICHLET BOUNDARY CONDITIONS. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2013;2(2):49-70. Available from: https://sid.ir/paper/243888/en

IEEE: Copy

ALI REZA SARAKHSI, MOHAMMAD JAHANSHAHI, and MOJTABA SARAKHSI, “INVESTIGATION OF APPROXIMATE SOLUTION OF MATHEMATICAL MODEL OF SINGULAR PERTURBATION PROBLEM OF INCLUDING SECOND ORDER LINEAR EQUATION WITH VARIABLE COEFFICIENTS AND DIRICHLET BOUNDARY CONDITIONS,” ADVANCES IN MATHEMATICAL MODELING, vol. 2, no. 2, pp. 49–70, 2013, [Online]. Available: https://sid.ir/paper/243888/en

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