Mathematical models on the basis of fundamental trigonometric splines

V. P. Denusiuk, O. V. Nehodenko

Abstract


The paper considers some systems of fundamental functions which are easy to be used in the problems for ordinary differential equations. The most well-known systems of fundamental functions include Lagrange system of fundamental functions and the complete systems even and odd fundamental trigonometric polynomials. However, there are some other systems of fundamental functions on analytical grid, including the systems of polynomial fundamental splines and complete trigonometric even and odd fundamental splines. Some of these systems are considered in this paper.

Keywords


funfamental functions; Lagrange functions; ordinary differential equations; simple polynomial splines; trigonometric splines; mathematical models

References


Denusiuk V. P. (2007). Splines and signals. Kyiv: VÌPOL (in Ukr.)

Denusiuk V. P. (2017). Trigonometric series and splines. Kyiv: NAU (in Ukr.)

Zenkevych O. Morgan K. (1986). Finite elements and approximation. Moscow: Nauka (in Rus.)

Denusiuk V. P. (2015). Fundamental functions and trigonometric splines. Kyiv: VÌPOL (in Ukr.)

Fletcher K. (1988). Numerical methods based on the Galerkin method. Moscow: Mur (in Rus.)

Denusiuk V.P., Rybachuk L. V., Nehodenko O. V. (2014). The construction of approximate solutions of boundary value problems for ordinary differential equations in the form of trigonometric polynomials. Problems of informatization and management, 1(45), 37-42.

Denusiuk V.P., Nehodenko O. V. (2016). Trigonometric splines and their applications for solving some problems of celestial mechanics. Visn.Astr.shkoly (Herald of the astronomical school), 12(1), 62-66.

Denusiuk, V.P. Nehodenko O.V., Influence of smoothness interpolation trigonometric splines on interpolation accuracy // Ukrainian Food Journal. 2013. Volume 2. Issue 4 http://www.ufj.ho.ua/


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