Asymptotic Forms and Algebraic Diierential Equations Asymptotic Forms and Algebraic Diierential Equations Asymptotic Forms and Algebraic Diierential Equations

We analyse the complexity of a simple algorithm for computing asymptotic solutions of an algebraic diierential equation. This analysis is based on a computation of the number of possible asymptotic monomials of a certain order, and on the study of the growth of this number as the order of the equation grows. Comportements asymptotiques et equations dii erentielles alg ebriques R esum e Nous analysons la complexit e d'un algorithme simple de calcul des solutions asymptotiques d' equations dii erentielles alg ebriques. L'analyse est bas ee sur la d etermination du nombre de mon^ omes asymptotiques d'ordre donn e, et sur l' etude de la croissance de ce nombre lorsque l'ordre de l' equation cro^ t. We analyse the complexity of a simple algorithm for computing asymptotic solutions of an algebraic diierential equation. This analysis is based on a computation of the number of possible asymptotic monomials of a certain order, and on the study of the growth of this number as the order of the equation grows.