A collocation method based on incomplete even and odd trigonometric splines is developed for first boundary value problems of linear ODEs and illustrated on three examples.
Polynomial and trigonometric splines
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abstract
Classes of simple polynomial and simple trigonometric splines given by Fourier series are considered. It is shown that the class of simple trigonometric splines includes the class of simple polynomial splines. For some parameter values, the polynomial splines coincide with the trigonometric ones; this allows to transfer to such trigonometric splines all the results obtained for polynomial splines. Thus, it was possible to combine two powerful theories - the theory of trigonometric Fourier series and the theory of simple polynomial splines. The above material is illustrated by numerous examples.
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Incomplete (even and odd) trigonometric splines in the problems of constructing approximate solutions of second order linear differential equations
A collocation method based on incomplete even and odd trigonometric splines is developed for first boundary value problems of linear ODEs and illustrated on three examples.