Modified Semi-Analytical Approach for Duffing Equation-Reference-Cited by-同舟云学术

Modified Semi-Analytical Approach for Duffing Equation

Published:2024-06-01 Issue:2 Volume:18 Page:300-306
ISSN:2300-5319
Container-title:Acta Mechanica et Automatica
language:en
Short-container-title:

Author:

Amara Um E¹^ORCID,Rehman Shahida²^ORCID,Abbas Mujahid¹²^ORCID,Rehman Jamshaid Ul²^ORCID

Affiliation:

1. Department of Mathematics , Government College University , Lahore-54600 , Pakistan

2. Abdus Salam School of Mathematical Sciences , Government College University , Lahore-54600 , Pakistan

Abstract

Abstract This research endeavour-investigates the enhanced adaptation of the Laplace-based variational iteration method (VIM) tailored specifically for tackling the Duffing Equation. This is accomplished by incorporating the Lagrange multiplier as a strategic tool to effectively address the inherent natural frequency within the Duffing Equation. Using a meticulous comparative analysis, here are juxtapose the analytical outcomes generated by the modified VIM approach with the numerical solution obtained through the application of the renowned Runge-Kutta Fehlberg method (RKF45), implemented by using the powerful mathematical software, MAPLE. Furthermore, by exploring the profound influence of diverse initial conditions on the resulting solution, a diverse array of distinct graphical representations is presented.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/ama-2024-0033

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