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Uniformly convergent methods for singularly perturbed problems
Author(s) -
Uzelac Zor.,
Surla Kat.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.199807815119
Subject(s) - mathematics , singular perturbation , equidistant , type (biology) , a priori and a posteriori , nonlinear system , piecewise linear function , quadratic equation , boundary value problem , perturbation (astronomy) , mathematical analysis , geometry , ecology , philosophy , physics , epistemology , quantum mechanics , biology
The present paper deals with boundary layer problem which represents the mathematical model for a large scale of practical problems in dynamics, fluid mechanics, chemistry and biology. The aim of this paper is to construct the approximate solution of the given problem in the form of quadratic splines on a simple piecewise equidistant mesh of Shishkin type and on a mesh of Bakhvalov type, which is a graded mesh specially constructed a priory to fit the problem. In the linear case we prove that the method is almost second order accurate, uniformly in the perturbation parameter, on the mesh of Shishkin type. Presented numerical experiments indicate the same result in the nonlinear case, while the second order of accuracy can be achieved on the mesh of Bakhvalov type.