Abstract
This paper presents a method for constructing polynomial approximations of the solutions of nonlinear initial value systems of differential equations. Given an a priori chosen accuracy, the degree of the vector polynomial can be adapted so that the approximate solution has the required precision. The method is based on the AI-method of Dzyadyk developed for the scalar case, and the computational cost is shown to be competitive with other methods. © 2011 Elsevier Inc. All rights reserved.
