Open AccessAPPLICATION OF FUNCTIONAL RELATIONS TO MODELING BY MEANS OF DIFFERENTIAL EQUATIONS
Author(s) -
E. Kenenbaev,
Dzh. A. Akerova,
L. Askar kyzy
Publication year - 2020
Publication title -
vestnik kyrgyzskogo gosudarstvennogo universiteta stroitelʹstva, transporta i arhitektury im.n.isanova/n.isanov atyndagy kyrgyz mamlekettik kuruluš,transport žana arhitektura universitetinin žarčysy
Language(s) - English
Resource type - Journals
eISSN - 1694-8181
pISSN - 1694-5298
DOI - 10.35803/1694-5298.2020.3.454-458
Subject(s) - mathematics , differential equation , partial differential equation , mathematical analysis , polynomial , lagrange polynomial , interpolation (computer graphics) , computer science , animation , computer graphics (images)
Modeling by means of differential equations is considered in the paper. Their solutions are constructed on the base of functional relations connecting values of a solution of the equation in different points (infinite or finite set of values). For examples, even, odd and periodical solutions, Vallée-Poussin’s assertion, Lagrange interpolation polynomial, Hermite interpolation polynomial, spline-functions for ordinary differential equations, Asgeirsson’s identity and its generalizations for partial differential equations of hyperbolic type, “mean value” for partial differential equations of elliptic type are considered. Also, if an equation is close to one of considered types then an assertion is to be fulfilled approximately. Some estimations are found for such examples. An application of such relations to investigate some problems of interpolation and extrapolation is demonstrated.