A Telescoping Decomposition Approach for Solving the Logistic Differential Equation

This paper investigates the application of the Telescoping Decomposition Method (TDM) to the Logistic Differential Equation (LDE) with the objective of obtaining accurate approximate solutions and benchmarking performance against established techniques. Methodologically, TDM is applied to two test cases, and the resulting approximations are compared with the exact solution and with those produced by the Elzaki Adomian Decomposition Method (EADM). The key findings show that TDM yields solutions in close agreement with the exact solution, with absolute errors reported as minimal (specific values not provided), and that it outperforms EADM in both accuracy and convergence rate while eliminating the need for repeated integral transforms. The study concludes that TDM is a simple, reliable, and computationally efficient approach for the LDE. The contribution and implication are that TDM offers a practical alternative for solving nonlinear differential equations and is readily extendable to more complex models.