Abstract
In Nipp, [this Journal, 17 (1986), pp. 512–532] error estimates were derived for the trajectories of a singularly perturbed autonomous system. The results are extensions of a classical result due to A. N. Tikhonov. In this paper we give the transfer of those estimates to the solutions of the autonomous system and an application to a problem in biomathematics. Special cases of our results are treated by Lebovitz and Schaar in Stud. Appl. Math., 54 (1975), pp. 229–260, 56 (1977), pp. 1–50, respectively. In order to transfer their estimates to the solutions, however, they introduce an artificial condition excluding a whole class of problems containing, e.g., the van der Pol relaxation oscillator as well as the example given in this paper.
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