On some questions arising in numerical realization of amplitude-phase methods

For computing rapidly oscillating solutions of certain second order differential equations a new version of amplitude-phase methods has recently been proposed in 11]. Error estimates were given to approximate solutions for large arguments in 15]. One of the most important points in these methods is the introduction of Prüfer transformation modified by auxiliary functions. Their appropriate choice makes the methods applicable and efficient. When implementing and applying the methods to practical problems, we face some further questions. In this paper we describe and try to answer them. Efficiency of the methods is confirmed by numerical experiments on concrete problems. This revised version was published online in June 2006 with corrections to the Cover Date.