Efficient P-stable methods for periodic initial value problems (Q762894)

P-stable methods for the numerical integration of an initial value problem \(y''=f(x,y)\) are important if the required solution has an unknown period. In a previous paper [Numer. Math. 37, 355-370 (1981; Zbl 0488.65029)] the author has introduced a class of P-stable 2-step methods of Runge-Kutta type. In the present paper the author discusses some special formulae of orders 4 and 6 requiring respectively only 2 and 4 function evaluations per step.