INVESTIGATION OF BOUNDARY LAYERS OF SINGULAR PERTURBATION PROBLEM INCLUDING SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS

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SARAKHSI ALI REZA; JAHANSHAHI MOHAMMAD

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Paper Information

Journal: JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY) Year:2013 | Volume:13 | Issue:3 Page(s): 809-818

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Title

INVESTIGATION OF BOUNDARY LAYERS OF SINGULAR PERTURBATION PROBLEM INCLUDING SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS

Author(s)

SARAKHSI ALI REZA | JAHANSHAHI MOHAMMAD | Issue Writer Certificate

Keywords

BOUNDARY LAYER PROBLEMQ2

FUNDAMENTAL SOLUTIONQ2

NECESSARY CONDITIONSQ2

Abstract

In this papear, we produce the method for formation and recognizing boundary layers in singular perturbation problems. This method involves four step for localization of non-local boundary conditions to local case. For the given problem some sufficient and NECESSARY CONDITIONS are given for formation and non formation of boundary layers. Since the existence of boundary layers and their places has a direct relation with the structure of approximate solutions and uniform solutions, therefore the main purpose of this paper is recognition and formation of boundary layers in singular perturbation problems with non-local boundary conditions. This process will be done by using FUNDAMENTAL SOLUTION of adjoint given differential equation and NECESSARY CONDITIONS. In fact by using these NECESSARY CONDITIONS and given boundary conditions, we make an algebraic system. By solving this algebraic system by Cramer rule we obtain boundary values of unknown function. These values of unknown function are local boundary conditions. The mathematical model for this kind of problem usually 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.

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APA: Copy

SARAKHSI, ALI REZA, & JAHANSHAHI, MOHAMMAD. (2013). INVESTIGATION OF BOUNDARY LAYERS OF SINGULAR PERTURBATION PROBLEM INCLUDING SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS. JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY), 13(3), 809-818. SID. https://sid.ir/paper/43900/en

Vancouver: Copy

SARAKHSI ALI REZA, JAHANSHAHI MOHAMMAD. INVESTIGATION OF BOUNDARY LAYERS OF SINGULAR PERTURBATION PROBLEM INCLUDING SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS. JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY)[Internet]. 2013;13(3):809-818. Available from: https://sid.ir/paper/43900/en

IEEE: Copy

ALI REZA SARAKHSI, and MOHAMMAD JAHANSHAHI, “INVESTIGATION OF BOUNDARY LAYERS OF SINGULAR PERTURBATION PROBLEM INCLUDING SECOND ORDER LINEAR DIFFERENTIAL EQUATION WITH NON-LOCAL BOUNDARY CONDITIONS,” JOURNAL OF SCIENCE (KHARAZMI UNIVERSITY), vol. 13, no. 3, pp. 809–818, 2013, [Online]. Available: https://sid.ir/paper/43900/en

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