Applying Differential Transform Method (DTM) to get Series Solution of Sixth Order Boundary Value Problems

Abstract

The Differential Transform Method (DTM) is an efficient and versatile analytical technique for obtaining series solutions to various Differential and Integral Equations. By significantly reducing computational effort while preserving accuracy, the DTM offers an attractive alternative to conventional methods. This paper demonstrates the efficacy and simplicity of the DTM through illustrative examples, focusing on higher-order Differential Equations with boundary value problems to derive precise series solutions. Furthermore, the DTM's adaptability and ease of implementation make it particularly suited for solving complex mathematical models. Its applications span diverse fields, including engineering, physics, and applied sciences, where it has been effectively utilized for analysing heat transfer, fluid dynamics, wave propagation, and electrical circuit problems. The findings underscore the potential of the DTM as a powerful tool for tackling challenging problems in theoretical and applied mathematics.