Application of Differential Transform Method to Delay Differential and Quadratic RICCATI Equations

Abstract

Delay differential equations (DDEs) and quadratic Riccati differential equations (QRDEs) play a crucial role in various scientific and engineering applications. Traditional analytical and numerical methods often face challenges in efficiently solving these equations due to their inherent complexity. In this study, we explore the Differential Transform Method (DTM) as an effective approach for obtaining approximate solutions to DDEs and QRDEs. DTM simplifies the computational process by transforming differential equations into algebraic equations, enabling rapid convergence and accuracy. We demonstrate the applicability of DTM through illustrative examples, comparing its performance with existing methods.