Modification of fourier approximation for solving boundary value problems having singularities of boundary layer type

Boris Semisalov, Georgy Kuzmin

Результат исследования: Научные публикации в периодических изданияхстатья по материалам конференции

Аннотация

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).

Язык оригиналаанглийский
Страницы (с-по)406-422
Число страниц17
ЖурналCEUR Workshop Proceedings
Том1839
СостояниеОпубликовано - 1 янв 2017

Fingerprint Подробные сведения о темах исследования «Modification of fourier approximation for solving boundary value problems having singularities of boundary layer type». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать