APPLICATION OF MULTI-STAGE HAM-PADÉTO SOLVE A MODEL FOR THE EVOLUTION OF COCAINE CONSUMPTION IN SPAIN

In this paper we obtain approximated analytical solutions for a mathematical model for the cocaine consumption in Spain using the Homotopy Analysis Method. The interest of the model is that, based on real data from Spanish Statistical Institute, it has been used to explain successfully the real evolution of the epidemic in Spain [18, 19]. First, we obtain with HAM an analytical approximation to the real solution of the model in the form of a power series of the time t. Second, we enlarge its domain of convergence applying the Padé after-treatment to the HAM solution. Finally, we apply multi-stage HAM-Padé to obtain an analytical approximate solution valid for the complete domain t in [∞,1]. This approximate solution has the form of three Padé approximants for the intervals [0, 50], [50, 150] and [150, ∞] years.