Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

Mulugeta Andualem,Atinafu Asfaw

doi:10.30538/oms2020.0134

Abstract

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

Highlights

I n the literature there are numerous integral transforms [1] that are widely used in physics, astronomy as well as in engineering
Many scientists still searching for new methods to solve such nonlinear initial value problems
In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method

Summary

Introduction

I n the literature there are numerous integral transforms [1] that are widely used in physics, astronomy as well as in engineering. In order to solve the differential equations, the integral transform was extensively used and there are several works on the theory and application of integral transform such as the Laplace, Fourier, Mellin, Hankel, Fourier Transform, Sumudu Transform, Elzaki Transform and Aboodh Transform. Aboodh Transform [2,3] was introduced by Khalid Aboodh in 2013, to facilitate the process of solving ordinary and partial differential equations in the time domain. This transformation has deeper connection with the Laplace and Elzaki Transform [4–6]. ZZ transform was successfully applied to integral equations and ordinary differential equations. The main objective of this article is to solve nonlinear ordinary differential equation using ZZ transform

The ZZ decomposition method

Conclusion