On the application of the Adomian-based methods

TL;DR

This paper critically examines two Adomian-based methods applied to the Chen-Lee-Liu equation, revealing they produce only Taylor expansions valid near zero time, thus limiting their applicability.

Contribution

It demonstrates that the Adomian-based methods yield Taylor series expansions, clarifying their limitations for solving the Chen-Lee-Liu equation.

Findings

Methods produce Taylor series expansions

Validity restricted to small time intervals

Highlights limitations of Adomian-based approaches

Abstract

We analyze a recent application of two Adomian-based approximate methods to the Chen-Lee-Liu equation. We prove that the outcome of these approaches is merely the Taylor expansion of the solution about $t=0$ and, consequently, they are valid only for sufficiently small values of the time variable $t$.