Bounds on asymptotic-numerical solvers for ordinary differential equations with extrinsic oscillation

In this paper we study an asymptotic-numerical solver for first-order ordinary differential equations with extrinsic oscillation. First we derive bounds on the terms of the asymptotic-numerical solver and estimate global errors of the method for a linear system. A numerical experiment is carried out to demonstrate the efficiency and robustness of this method for a linear system. Then the bounds on the terms of the asymptotic-numerical solver are also discussed for a nonlinear system and two numerical experiments are presented for that case.