A Review: Differential transform in numerical study of differential equations

Abstract

Differential equation plays an important role in understanding various phenomenon of science and engineering. Various methods have been developed by mathematicians to obtain a numerical solution of differential equations with minimum errors, transform methods are one of such numerical methods. Till present no transform methods claims to have zero error in obtaining the numerical or exact solution of the given differential equations. Few of well-known transform methods are Laplace transform, Sumudu transforms, Differential transform, Integral transform method etc. In this paper the review of Laplace transform is presented which is one of the tools used by scientists and researchers in finding the solution to their differential equation. In this work, 18 research papers of applications of Laplace transform have been studied and it is shown how this transform has been used by other researchers to obtain the exact solution of ordinary, partial and fractional differential equations. To present a literature review on application of Laplace transform is the main objective of this work.