engleski

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

This paper presents new procedure of numerical solving of initial-value problems. To obtain a response of a dynamic system, smooth finite functions Fup2(t) which belong to a class of Rvachev's basis functions Rbf are used. Because of infinite derivability of the functions Fup2(t), derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in numerical procedure. Accuracy and stability of the proposed numerical procedure are proved on an example of the single degree of freedom system. Critical time step was also determined. An algorithm for solving multiple degree of freedom systems by the collocation method was developed. Obtained numerical results show very good correspondence with an exact solution.

initial-value problems; Rvachev's basis functions; accuracy and stability; critical time step

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