Инд. авторы:	Semisalov B.V., Kuzmin G.A.
Заглавие:	Modification of Fourier approximation for solving boundary value problems having singularities of boundary layer type
Библ. ссылка:	Semisalov B.V., Kuzmin G.A. Modification of Fourier approximation for solving boundary value problems having singularities of boundary layer type // CEUR Workshop Proceedings. - 2017. - Vol.1839. - P.406-422. - ISSN 1613-0073.
Внешние системы:	РИНЦ: 31018499; SCOPUS: 2-s2.0-85020513805;
Реферат:	eng: A method for approximating smooth functions has been developed using non-polynomial basis obtained by mapping of Fourier series domain to the segment [1, 1]. High rate of convergence and stability of the method is justified theoretically for four types of coordinate mappings, the dependencies of approximation error on values of derivatives of approximated functions are obtained. Algorithms for expanding of functions into series with coupled basis composed of Chebyshev polynomials and designed non-polynomial functions are implemented. It was shown that for functions having high order of smoothness and extremely steep gradients in the vicinity of bounds of segment the accuracy of proposed method cardinally exceeds that of Chebyshev's approximation. For such functions method allows to reach an acceptable accuracy using only = 10 basis elements (relative error does not exceed 1 per cent).
Ключевые слова:	Coordinate mapping; Estimate of convergence rate; Fourier series; Non-polynomial basis; Singular perturbation; Small parameter; Boundary layers; Boundary value problems; Fourier series; Polynomials; Small parameter; Polynomial basis; Coordinate mapping; Convergence rates; Collocation method; Chebyshev polynomials; Mapping; Fourier transforms; Collocation method; Chebyshev polynomial; Boundary value problem; Singular perturbations;
Издано:	2017
Физ. характеристика:	с.406-422
Конференция:	Название: Международная конференция «Математические и информационные технологии, MIT-2016» Аббревиатура: MIT-2016 Город: Врнячка Баня, Будва Страна: Сербия, Черногория Даты проведения: 2016-08-28 - 2016-09-05 Ссылка: http://conf.nsc.ru/MIT-2016
Цитирование:	1. Kadalbajoo, M. K., Gupta, V.: A brief survey on numerical methods for solving singularly perturbed problems. Applied Mathimatics and Computation. 217(8), 3641- 3716 (2010). 2. Kreiss, H.-O., Nichols, N. K., Brown, D. L. Numerical methods for stiff two-point boundary value problems. SIAM J. Numer. Anal. 23 (2), 325-368 (1986). 3. Liseikin, V. D., Likhanova, Yu. V., Shokin, I. Numerical grids and coordinate transformations for the solution of singularly perturbed problems. Nauka. Novosibirsk (2007, in Russian). 4. Liu, W., Tang, T. Error analysis for a Galerkin-spectral method with coordinate transformation for solving singularly perturbed problems. Appl. Numer. Math. 38, 315-345 (2001). 5. Wang, Yi., Chen, S. A rational spectral collocation method for solving a class of parameterized singular perturbation problems. J. of Comput. and Appl. Math. 233, 2652-2660 (2010). 6. Babenko, K.I.: Fundamentals of numerical analysis. Regular and chaotic dynamics, Moscow-Izhevsk (2002, in Russian). 7. Jackson, D.: On Approximation by Trigonometric Sums and Polynomials. Trans. Amer. Math. Soc. 13, 491-515 (1912). 8. Dzydyk, V. K.: Introduction to the Theory of Uniform Approximation of Functions by Means of Polynomials. Nauka, Moscow (1977, in Russian). 9. Bakhvalov, N.S., Zhidkov, N.P., Kobel'kov, G.M.: Numerical methods. Textbook. Nauka, Moscow (1987, in Russian). 10. Boyd, J.: Chebyshev and Fourier Spectral Methods. Second Edition. University of Michigan (2000). 11. Orszag, S. A., Israeli, M.: Numerical simulation of viscouse incompressible flows. Ann. Rev. Fluid Mech. 6, 281-318 (1974).