On Approximate Solution of One Singular Perturbation Boundary Value Problem
Author(s):
Egor Konstantinovich Kulikov
St. Petersburg State University, Department of Parallel Algorithms,
Post-graduate student
Russia, 199034, Saint-Petersburg, Universitetskaya nab., 7/9
egor.k.kulikov@gmail.com
Anton Alexandrovich Makarov
St. Petersburg State University, Department of Parallel Algorithms,
Professor, Dr. Sci.
Russia, 199034, Saint-Petersburg, Universitetskaya nab., 7/9
a.a.makarov@spbu.ru
Abstract:
The paper considers the problem of approximation of a function that
is a solution of singular perturbation boundary value problem.
Such functions have huge boundary layer components, so the applying
classical algorithms to them leads to essential errors. We introduce
an approach that is a local approximation scheme based on minimal splines
on the Shishkin grid, where the coefficients of basis functions are calculated
as the values of de Boor-Fix type functionals. We also present the results of
numerical experiments showing that our approach allows obtaining
the approximation of high quality.
Keywords
- boundary layer components
- B-splines
- de Boor-Fix type functionals
- minimal splines
- Shishkin grids
References:
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