Taylor Series for Adomian Decomposition Method

TL;DR

This paper analyzes the use of Taylor series in Adomian's decomposition method for solving scalar PDEs, proposing a modification that simplifies coefficient calculation especially for nonautonomous equations.

Contribution

The paper introduces a modification to Adomian's decomposition method that simplifies the computation of Taylor coefficients for scalar PDEs.

Findings

Modified method facilitates easier calculation of Taylor coefficients.

Enhanced approach improves solutions for nonautonomous equations.

Illustrative examples demonstrate the method's effectiveness.

Abstract

In the paper we analyse the exact solutions to scalar PDEs obtained thanks to summable Taylor series provided by Adomian's decomposition method. We propose the modification of the method which makes the calculations of Taylor coefficients easier and more direct. The difference is essential for instance in case of nonautonomous equations and is illustrated by some exampl