A probabilistic approach to Adomian polynomials

Abstract

The Adomian decomposition method (ADM) is a powerful tool to solve several nonlinear functional equations and a large class of initial/boundary value problems. In this paper, we discuss a probabilistic approach to compute the Adomian polynomials (AP’s), which is the main part of the ADM. We provide a probabilistic interpretation for the AP’s, both for the one-variable and the multivariable case. We derive some new recurrence relations for the computation AP’s. Some suitable examples are discussed to show that the probabilistic approach to compute the AP’s is much simpler than the analytical or combinatorial approach.