Efficient and Accurate Solutions to Nonlinear Differential-Algebraic Equations Using Differential Transform Method and Bell Polynomials

This paper presents an efficient and accurate method for solving nonlinear differential-algebraic equations (DAEs) using the Differential Transform Method (DTM) and Bell polynomials. In this paper, research work introduces a novel approach to solving nonlinear differential algebraic equations (DAEs) by leveraging the Differential Transform Method (DTM) in conjunction with Bell polynomials. Nonlinear DAEs, which appear in many engineering and physical systems, present significant challenges due to their inherent complexity, including singularities and highly nonlinear behavior. The proposed method uses the Differential Transform Method for efficient computation of solutions and applies Bell polynomials to handle the nonlinearity more effectively. The method is tested on various problems, including those from control systems and mechanical engineering, with a focus on improving accuracy and reducing computational cost. Numerical examples demonstrate the practical application of the method, and comparisons with other well-known methods are provided. Results indicate that the proposed approach yields more accurate and efficient solutions for complex nonlinear DAE systems.