In this work, we present a new approach in the algorithm of the Adomian method for the resolution of nonlinear partial differential equations (PDE) with initial and boundary conditions. This new method is based on a combination of Adomian decompositional method and the idea of the successive approximation method [3]. We have shown that this new algorithm is convergent with a few number of iterations.

Adomian method, successive approximations, biomathematical modeling.