Two-step hybrid methods for periodic initial value problems (Q1101187)

For the numerical solution of the special second order initial value problem \(y''=f(t,y)\) the authors consider two-step methods with off-step points, which were originally proposed by \textit{J. R. Cash} [BIT 24, 248- 252 (1984; Zbl 0558.65053)]. The free parameters of the method are determined in such a way that the methods are P-stable and that the Jacobian of the nonlinear system can be expressed as a power of \((I- \gamma h^ 2\frac{\delta f}{\delta y})\). Numerical results are included.