Comparing Differential Transform Method (DTM) And SEJI Transform For Solving Ordinary Differential Equations With Variable Coefficients

Abstract

This study compares the Differential Transform Method (DTM) and the SEJI Integral Transform for solving ordinary differential equations (ODEs) with variable coefficients. The objective is to evaluate the performance of these methods by analyzing their accuracy and computational efficiency. Two examples of second-order linear ODEs with variable coefficients were selected as test cases. The study begins by solving the ODEs using DTM and SEJI separately, employing Maple software for computation and analysis. Numerical and graphical comparisons were made to assess the closeness of the approximate solutions to the exact solutions. Results from both methods were then analyzed based on absolute error and computational feasibility. Findings reveal that both DTM and SEJI closely approximate the exact solutions, with SEJI achieving perfect numerical accuracy in both test cases. DTM, while highly accurate for smaller intervals, shows an increase in absolute error as the interval size grows. Despite this, DTM is computationally efficient and versatile, especially for problems where integral transformations may be challenging to apply. In conclusion, the SEJI Integral Transform demonstrates superior accuracy, while DTM offers computational simplicity and flexibility.