Abstract. The amplitude-phase method has been proposed recently for computing the rapidly oscillating solutions of second-order ordinary differential equations on a semi-infinite interval in [1]. In the paper error estimates are obtained for this. The method and the error estimations introduced below can be applied to a wide class of problems. The numerical solutions are evaluated by solving differential problems posed for auxiliary functions on a finite interval, only. The error estimation problem of approximations at the right end point is reduced to the estimation of certain improper integrals. By proving the Leibniz property of sequences closely related to these integrals, an a priori estimate will be given. As a direct consequence of the result, a new definition of the shifting function will be introduced which allows the simultaneous stabilization of the auxiliary functions.

AMS Subject Classification (1991): 65D20, 65L70

Received October 9, 1996. (Registered under 5790/2009.)