Polynomial approximation of nonlinear differential systems with prefixed accuracy

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.Chen Charpentier, BM.; Jódar Sánchez, LA.; Telyakovskiy, AS. (2011). Polynomial approximation of nonlinear differential systems with prefixed accuracy. Applied Mathematics and Computation. 218(5):1650-1657. doi:10.1016/j.amc.2011.06.044S16501657218