Solving Third Order Ordinary Differential Equation (ODE) by using Differential Transform Method (DTM)

Abstract

In this research, a semi analytical solution called differential transform method (DTM) was used to solve Third Order Ordinary Differential Equation (ODE). The Third Order ODE's approximative solutions were discovered using Maple 2020. This method has been shown to reduce computational work and save time. The numerical result derived by DTM is compared with the result of Bernstein Polynomials Method (BPM), Adaptive Polynomial Method (APM) and the Modified Adomian Decomposition Method (MADM) which are based on earlier research in order to evaluate how closely the value matches the exact value. After comparing the results of the various approaches, it was found that DTM provided the closest approximation for solving Third Order ODEs. This outcome depends on the kind of Third Order ODE and the number of terms in the DTM. For solving Third Order ODE, a few terms of DTM are recommended to obtain the approximate value. DTM have successfully solved three example and regarded as the simplest method to use and may solve differential problems since it requires less computational to produce an approximation to exact value.