Improving the Differential Transform Method for Nonlinear Oscillatory Systems: Theory, Algorithms, and Applications
Keywords:
Differential Transform Method, Padé Approximant, Nonlinear Oscillatory Systems, Linear Differential Equations, Laplace Transform, Series AccelerationAbstract
This study looks into the use of the Differential Transform Method (DTM) to analyze linear, weakly nonlinear and nonlinear oscillatory differential equation systems. Recognizing that standard DTM solutions may lack the inherent periodic nature of oscillatory systems, we propose an improved method that uses Padé approximants and Laplace transforms to recover periodicity and extend convergence domains. The methodology is systematically described and validated using representative examples to demonstrate its efficacy, increased accuracy, and computational efficiency. The findings indicate that DTM, particularly when combined with aftertreatment techniques, is a powerful and practical tool for solving a wide range of differential equations in mathematical physics and engineering.
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