Soluciones Analíticas para Ecuaciones Ordinarias no Lineales

Abstract

In this paper the analytical solution of nonlinear ordinary differential systems is addressed. The problems are classical in the related literature and exhibit chaotic behavior in certain ranges of the involved parameters despite being simple-looking deterministic systems. The solutions are approached by means of algebraic series in the time variable that lead to elementary recurrence algorithm. This is an alternative to the standard numerical techniques and ensures the theoretical exactness of the response. The desired numerical precision is attained using time steps several times larger than the usual ones. Two examples are included: a) projectile motion and, b) n bodies with gravitational attraction. Trajectories diagrams are shown. An available analytical solution may be an additional tool within the standard qualitative analysis.
The solution of higher order problems and others governed by partial differential equations is under study