Simple Parametrization Methods for Generating Adomian Polynomials

TL;DR

This paper introduces two simple, efficient parametrization methods for calculating Adomian polynomials, applicable to various nonlinear operators including complex cases like Navier-Stokes, with minimal computation and easy implementation.

Contribution

The paper presents novel parametrization techniques for Adomian polynomials that simplify calculations and extend to multivariable cases, improving computational efficiency and applicability.

Findings

Methods require minimal computation

Extended to multivariable nonlinear operators

Explicit expressions derived for many examples

Abstract

In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.