Astronomical School’s Report, 2016, Volume 12, Issue 1, Pages 62–66

https://doi.org/10.18372/2411-6602.12.1062
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UDC 519.61(045)

Trigonometric splines and their applications to solve some problems of celestial mechanics

Denysiuk V.P., Negodenko Е.V.

National Aviation University, Ukraine

Abstract

There was suggested a method of constructing approximate solutions of the first boundary problem for ordinary differential equations of the second order with variable coefficients in trigonometric polynomials using the phantom nodes method. Unknown parameters are determined by collocation. An example is given; it is shown that the relative error of the solution has reduced times with the introduction of phantom nodes.

Keywords: celestial bodies; differential equations; phantom nodes; splines

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