Applications Of The Differential Transform Method In Handling Weakly Nonlinear Differential Equation Systems

In order to solve differential equations, the Differential Transform Method (DTM) has gained widespread acceptance due to the fact that it is semi-analytical in nature and has a low overall computing complexity. Biological, physics, and engineering models are examples of situations that typically include weakly nonlinear differential equation systems. This study investigates the utility of DTM in controlling these types of systems. Through the use of linearization techniques, recursive series expansion, and hybrid modifications, the paper analyzes the mathematical foundations of DTM and demonstrates how it may be adapted to nonlinear systems. It is possible to validate the efficacy and accuracy of DTM by using benchmark nonlinear systems such as the Duffing oscillator and predator-prey models. DTM is able to successfully control mild nonlinearities and provide correct approximations with a minimal number of iterations, as shown by previous findings. Convergence enhancement strategies for chaotic or highly nonlinear systems are being investigated as part of this research.