IMPROVING Α-Parameterized DIFFERENTIAL TRANSFORM METHOD WITH DANDELION OPTIMIZER FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this manuscript, we aim to address Ordinary Differential Equations (ODEs) by α-Parameterized Differential Transform Method (α-PDTM). Additionally, we seek to enhance the effectiveness of α-PDTM by incorporating the Dandelion Optimizer (DO). The DO plays a crucial role in optimizing the parameter α, ensuring its adjustment and modification to secure the most favorable value. This refinement results in a more accurate approximation compared to conventional methods. The proposed approach, referred to as (αDO-PDTM), demonstrates a solution distinguished by its reliability and efficiency, as determined through the computation of Maximum Absolute Error (MAE) and the Mean Square Errors (MSE).