초록 close

This paper presents a numerical procedure for solving initial-value problems using the specialfunctions which belong to a class of Rvachevs basis functions Rbf based on algebraic and trigonometricpolynomials. Because of infinite derivability of these functions, derivatives of all orders, required bydiferential 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 singledegree of freedom system. Critical time step was also determined. An algorithm for solving multipledegree of freedom systems by the collocation method was developed. Numerical results obtained by Rbffunctions are compared with exact solutions and results obtained by the most commonly used numericalprocedures for solving initial-value problems.