Zero-dissipative phase-fitted hybrid methods for solving oscillatory second order ordinary differential equations

In this paper, zero-dissipative phase-fitted two-step hybrid methods are developed for the integration of second-order periodic initial value problems. The phase-fitted hybrid methods are constructed using similar approaches introduced by Papadopoulos et al. [1]. This new methods are based on the existing explicit hybrid methods of order four and six. Numerical illustrations indicate that the new methods are much more efficient than the existing methods.