Analytical Iteration Method Applied to a Class of First Order Nonlinear Evolution Equations in Science

Edmond Obiem Odok; Liberty Ebiwareme

Title:
Analytical Iteration Method Applied to a Class of First Order Nonlinear Evolution Equations in Science

Authors:
Liberty Ebiwareme | Edmond Obiem Odok

Cite This Article :

Liberty Ebiwareme | Edmond Obiem Odok "Analytical Iteration Method Applied to a Class of First Order Nonlinear Evolution Equations in Science" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3, April 2022, pp.132-139, URL: https://www.ijtsrd.com/papers/ijtsrd49491.pdf

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Abstract :
In this research paper, we apply the novel Temimi-Ansari method to six first order nonlinear partial differential equations for exact solution namely: Burger’s equation, Fisher’s equation, Schrodinger equation, wave equation, advection equation and KDV equations respectively. Unlike other semi-analytical iterative methods, this method doesn’t require linearization, perturbation, discretization, or the calculation of an Adomian polynomials for nonlinear terms in the Adomian decomposition method (ADM). It gives the closed form solution of the problem if it exists in finite steps of a converging series that’s computationally convenient, easy to obtained and elegant. It solves the inherent problem of dealing with the nonlinear term in a straightforward way without stress. The result obtained revealed, all the chosen problems give rise to their closed form solution in simple steps which confirmed the method is powerful, reliable and has wide applicability to other nonlinear problems.

Keywords :
KDV Equation, Advection equation, Schrödinger equation, Burger’s equation, Fisher’s equation, Temimi-Ansari method

Publication Details:

Unique Identification Number : IJTSRD49491

Published In : Volume-6 | Issue-3, April 2022

Page Number(s) : 132-139

Publisher Name : IJTSRD | www.ijtsrd.com | E-ISSN 2456-6470

Copyright © 2019 by author(s) and International Journal of Trend in Scientific Research and Development Journal. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0) (http://creativecommons.org/licenses/by/4.0)

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