Numerical solving of initial-value problems by R-bf basis functions

This paper presents a numerical procedure for solving initial-value problems using the special functions which belong to a class of Rvachev\'s basis functions R-bf based on algebraic and trigonometric polynomials. Because of infinite derivability of these functions, derivatives of all orders, required by differential equation of the problem and initial conditions, are used directly in the numerical procedure. The accuracy and stability of the proposed numerical procedure are proved on an example of a 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. Numerical results obtained by R-bf functions are compared with exact solutions and results obtained by the most commonly used numerical procedures for solving initial-value problems.<br />