About Finite Series, connected with Orthogonal Finite Functions, in Fourier Method

Title	About Finite Series, connected with Orthogonal Finite Functions, in Fourier Method
Authors	V. L. Leontiev¹ ¹Peter the Great St.Petersburg Polytechnic University
Annotation	The generalization of Fourier method is connected with using of orthogonal compactly supported functions. The generalization is produced on the example of first boundary value problem for region with curvilinear boundary. Formed sequence of finite Fourier series converges to exact solution in every moment of time. The method gives analytical solutions in form of finite Fourier series, which have the structure similar to the structure of exact solution. It opens new possibilities of classical Fourier method for task in region with curvilinear boundary. Similar generalization of Fourier method is possible for other boundary value problems and for 3 dimensions.
Keywords	Method of differentiation of variables, Fourier method, orthogonal finite functions, finite series, boundary value problem, domain with curvilinear boundary, own values of operator, own functions of operator.
Citation	Leontiev V. L. ''About Finite Series, connected with Orthogonal Finite Functions, in Fourier Method'' [Electronic resource]. Proceedings of the XIV International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 9-12, 2019). Saransk: SVMO Publ, 2019. - pp. 124-130. Available at: https://conf.svmo.ru/files/2019/papers/paper36.pdf. - Date of access: 23.04.2024.