Correlation between Adomian and Partial Exponential Bell Polynomials

TL;DR

This paper explores the relationship between Adomian polynomials and partial exponential Bell polynomials, deriving recurrence relations and identities that facilitate explicit expressions for nonlinear operators.

Contribution

It introduces new recurrence relations and identities linking Adomian and Bell polynomials, enhancing analytical tools for nonlinear operator decomposition.

Findings

Derived recurrence relationships among partition vectors of Bell polynomials.

Expressed Adomian polynomials explicitly using Bell polynomials.

Obtained new identities for Bell polynomials via differential equations.

Abstract

We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the $n$-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using Adomian decomposition method.