DISSIPATIVE TRIGONOMETRICALLY-FITTED METHODS FOR SECOND ORDER IVPs WITH OSCILLATING SOLUTION

In this paper a dissipative trigonometrically-fitted two-step explicit hybrid method is developed. This method is based on a dissipative explicit two-step method developed recently by Papageorgiou, Tsitouras and Famelis.6 Numerical examples show that the procedure of trigonometrical fitting is the only way in one to produce efficient dissipative methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions.