Elzaki based hybrid method for the solutions of nonlinear integer order differential equations

Abstract

This paper is concerned with the solutions of nonlinear differential equations by a proposed hybrid method that is developed through a well-considered integration of a Laplace-type integral transform; Elzaki transform into a semi-analytical method called Adomian decomposition method. This hybrid approach is tagged Elzaki Based Hybrid Method (EBHM). To apply the new method, Elzaki transform of the terms in the given nonlinear differential equations is first taken, while Adomian polynomial is used to decompose the nonlinear term that may be encountered. To get the desired result, inverse Elzaki transform is made use of at the final stage of the computation. To validate the proposed method, it is used to solve selected problems in the existing literature. The method gives exact solutions for all the problems considered with reduced computational volume. All the coding and computations are carried out with Mathematica 13.3.