Comparison Differential Transform Method and Elzaki Transform for Solving Linear Ordinary Differential Equations with Constant Coefficients

Abstract

This research aims to demonstrate solutions for linear ordinary differential equations (ODEs) using the Differential Transform Method (DTM). Numerical results, including graphs and absolute errors, will be obtained using MATLAB R2024a. The primary motivation for using DTM lies in fast convergence rate and its ability to provide accurate results close to the exact solution. DTM successfully solves two examples of linear ODEs and requires minimal computational effort. Using the numerical solutions obtained via MATLAB R2024a, the results will be compared with those derived from Elzaki transform. The absolute errors of both method will be analyzed and discussed. Although the Elzaki transform demonstrates higher accuracy than DTM, this research does not solely focus on accuracy but also aims to compare various aspects of these two methods.