Adomian decomposition method reformulated using dimensionless nonlinear perturbation theory

TL;DR

This paper reformulates the Adomian decomposition method using dimensionless nonlinear perturbation theory to address convergence and accuracy issues, providing a more physically interpretable framework for solving nonlinear equations.

Contribution

It introduces a new reformulation of ADM based on nonlinear perturbation theory, resolving fundamental mismatches and enhancing understanding of convergence and stability.

Findings

Improved convergence analysis of ADM

Enhanced physical interpretation of series solutions

Addressed mismatch in expansion parameter order

Abstract

The Adomian decomposition method (ADM) is a universal approach to solving governing equations in various engineering and technological applications. The applicability of the ADM is almost limitless due to its universal applicability, but its convergence rate and numerical accuracy are sensitive to the number of truncated terms in series solutions. More importantly, Adomian formalism still holds unresolved issues regarding the mismatch of the order of the expansion parameter. The current work provides an in-depth analysis of Adomian's decomposition method, Lyapunov's stability theory, and the nonlinear perturbation theory to resolve the fundamental mismatch with physical interpretation.