IJPAM: Volume 56, No. 1 (2009)

Invited Lecture Delivered at
Fifth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2008)


A. Shayganmanesh (Golbabai)
Department of Applied Mathematics
Faculty of Mathematics
Iran University of Science and Technology
Narmak, Tehran, 16844, IRAN
e-mail: [email protected]

Abstract.In this paper, we consider in which region the perturbations are operative over very narrow region across which the dependent variables undergo very rapid changes. These narrow regions frequently adjoin the boundaries of the domain of interest, owing to the fact that the small parameter multiplies the highest derivatives, consequently, they are usually referred to as boundary layers.

The main aim of the present work is to establish fairly wide conditions under which the asymptotic matching principle [#!1!#] is correct. Two expansions are given in which one tries to recover the missing data by exploiting the fact that the two series, which are to be asymptotic expansion (in more or less adjacent regions) of the unknown function $f(x,\varepsilon)$ must somehow be related to each other. Finally we have shown that the structure of the composite expansion based on matching principle is in good agreement with exact solution of the problem.

Received: August 13, 2008

AMS Subject Classification: 76R05

Key Words and Phrases: inner layer, asymptotic expansion, singular perturbation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1