Numerical analysis of the Adomian method and its application to chaotic systems*

Experimental numerical analysis of the analytical series technique to solve nonlinear systems based on the so-called Adomian polynomials expansions will be presented here. Unlike standard difference methods like Runge-Kutta schemes of various orders, the Adomian method enables to compute a single approximation on relatively long time intervals. The corresponding lengths can be combined with the order of the polynomial expansions, thereby providing variety of trade-offs between them to achieve similar accuracy. The generalized Lorenz chaotic system has been chosen as a testing platform.