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Numerical solving of an initial-value problem by Rbf basis functions of trigonometric polynomials class

This paper presents numerical procedure of solving of initial-value problem using the special basis functions yw, h(t). These are the functions of Rvachev's basis functions Rbf class from the vector space which contains trigonometric polynomials. Approximation properties of functions yw, h(t) enable that by their application in numerical determining of the response of a dynamic system, an exact solution of free vibrations without damping is obtained. The collocation method is applied in the numerical procedure. The proposed procedure is illustrated on an example of the forced vibrations of a material point without damping. For an approximation of the disturbing force, basis functions Fupn(t), also of Rbf class, are applied. The numerical solution, which completely corresponds to an exact solution, was obtained.

initial-value problem; Rvachev's basis functions; collocation method

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