Comparison of Differential Transform Method and Sawi Transform Method For Solving System of Ordinary Differential Equations

Abstract

Systems of Ordinary Differential Equations (ODEs) are integral to modeling phenomena in engineering, science, and technology. This paper evaluates the Differential Transform Method (DTM) and the Sawi Transform Method (STM) for solving linear system of ODEs, focusing on their computational and practical efficiencies. Examples of system of linear ODEs are solved using DTM, and the results are compared with exact solutions and STM found from previous research. MATLAB was utilized for numerical implementation and graphical outputs. DTM, a semi-analytical technique, demonstrated simplicity and flexibility when expanded to higher orders. STM, an analytical method, achieved exact solutions but required higher computational resources and intricate inverse transformations. Comparative results showed that while STM excels in precision for simpler systems, DTM offers simplicity and applicability for complex and higher-order problems. This study offers insights into the suitability of DTM and STM, emphasizing their roles in enhancing computational efficiency and solution accuracy for technical and engineering challenges.