$\alpha$-Parameterized Differential Transform Method

TL;DR

This paper introduces an $oldsymbol{oldsymbol{ extalpha}}$-parameterized differential transform method, a new numerical algorithm that improves coefficient calculation in Taylor polynomial approximations, demonstrating efficiency and reliability through numerical examples.

Contribution

It presents a novel $oldsymbol{ extalpha}$-parameterized differential transform method that enhances the traditional approach with a new coefficient calculation technique.

Findings

The method is simple and effective.

Numerical examples confirm its efficiency.

It is reliable for solving differential equations.

Abstract

In this paper we propose a new version of differential transform method (we shall call this method as $\alpha$-parameterized differential transform method), which differs from the traditional differential transform method in calculating coefficients of Taylor polynomials. Numerical examples are presented to illustrate the efficiency and reliability of own method. The result reveal that $\alpha$-Parameterized differential transform method is a simple and effective numerical algorithm.