The Convergence of the Differential Transform Method for Solving Semi-Explicit Index-2 Differential Algebraic Systems

This paper investigates the convergence of the differential transform method for solving differential algebraic systems. Differential algebraic systems, which combine differential and algebraic equations, pose significant challenges due to their inherent structural constraints and index-related complexities. The study presents a comprehensive convergence analysis of differential transform method, emphasizing the conditions required for the method to produce accurate and reliable solutions. Additionally, the multi-stage differential transform method is employed to extend the convergence interval, thereby enhancing the method's applicability to more complex systems. Numerical examples illustrate the effectiveness of the proposed approach, demonstrating its accuracy and computational efficiency in solving differential algebraic systems. The results confirm that the differential transform method, along with its multi-stage variant, is a powerful tool for obtaining approximate solutions to differential algebraic systems while preserving their inherent properties.