Convergence of Fourier Method connected with Orthogonal Splines

Название	Convergence of Fourier Method connected with Orthogonal Splines
Авторы	Leontiev V. L.¹ ¹World-Class Research Center for Advanced Digital Technologies at Peter the Great St. Petersburg Polytechnic University
Аннотация	Fourier series, Fourier method and spline approximations have wide scopes. The generalized Fourier method associated with the use of finite Fourier series and orthogonal splines was applied earlier for solving the parabolic initial boundary value problems for regions with curvilinear boundaries. Here another analogous generalized Fourier method is applied for solving parabolic initial boundary value problems in noncanonical regions and the investigation of convergence of this method is proposed. The study of convergence is based on the theory of finite difference methods. This method gives solutions in form of finite Fourier series which structure is similar to that of partial sums of an infinite Fourier series of an exact solution. As a number of grid nodes increases in a region, a finite Fourier series approach an exact solution of a parabolic initial boundary value problem. The investigation of convergence shows efficiency of the algorithm of the generalized Fourier method in solving parabolic initial boundary value problems for noncanonical regions. This method yields the approximate analytical solutions in the form of the sequence of finite Fourier series. The use of orthogonal splines brings together numerical and analytical methods – finite difference methods and the Fourier method, expanding the scope of their applications.
Ключевые слова	parabolic initial boundary value problems, noncanonical regions, curvilinear boundary, the method of separation of variables, finite Fourier series, orthogonal splines.
Образец ссылки на статью	Leontiev V. L. Convergence of Fourier Method connected with Orthogonal Splines [Электронный ресурс] // Математическое моделирование, численные методы и комплексы программ: XI Международная научная молодежная школа-семинар имени Е.В. Воскресенского (Саранск, 26-28 июля 2024 г.). - С. 226-228. Режим доступа: https://conf.svmo.ru/files/2024/papers/paper44.pdf. - Дата обращения: 16.10.2024.

МАТЕРИАЛЫ НАУЧНЫХ КОНФЕРЕНЦИЙ И ШКОЛ-СЕМИНАРОВ

Convergence of Fourier Method connected with Orthogonal Splines

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