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Approximate solution of ordinary differential equations using Chebyshev seriesстатья
Дата последнего поиска статьи во внешних источниках: 14 апреля 2016 г.
- Авторы: Arushanyan O.B., Volchenskova N.I., Zaletkin S.F.
- Журнал: Siberian Electronic Mathematical Reports
- Том: 7
- Год издания: 2010
- Первая страница: 122
- Последняя страница: 131
- Аннотация: An approximate method to solve the Cauchy problem for normal and canonical systems of second-order ordinary differential equations is proposed. The method is based on orthogonal expansions of the solution and its derivative in shifted series of Chebyshev polynomials of the first kind at the integration step. The corresponding equations are constructed for the approximate values of Chebyshev coefficients in the right-hand side of the system under study. An iterative process for solving these equations is described and some sufficient conditions of its convergence are considered. Several error estimates for the Chebyshev coefficients and for the solution are given with respect to the size of the integration step. Ключевые слова: ordinary differential equations, numerical methods.
- Добавил в систему: Арушанян Олег Багратович