Modified Semi-Analytical Approach for Duffing Equation

Um E. Amara; Shahida Rehman; Mujahid Abbas; Jamshaid Ul Rehman

doi:10.2478/ama-2024-0033

Modified Semi-Analytical Approach for Duffing Equation

Um E. Amara, Shahida Rehman, Mujahid Abbas, Jamshaid Ul Rehman

Government College University Lahore

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	300-306
Number of pages	7
Journal	Acta Mechanica et Automatica
Volume	18
Issue number	2
DOIs	https://doi.org/10.2478/ama-2024-0033
Publication status	Published - 1 Jun 2024
Externally published	Yes

Keywords

Simulink model
mechanical vibration
modified variational iterative method
nonlinear dynamics

ASJC Scopus subject areas

Control and Systems Engineering
Mechanical Engineering

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10.2478/ama-2024-0033

Cite this

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title = "Modified Semi-Analytical Approach for Duffing Equation",

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.",

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AU - Rehman, Shahida

AU - Abbas, Mujahid

AU - Rehman, Jamshaid Ul

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N2 - 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.

AB - 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.

KW - Simulink model

KW - mechanical vibration

KW - modified variational iterative method

KW - nonlinear dynamics

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JO - Acta Mechanica et Automatica

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IS - 2

ER -

Modified Semi-Analytical Approach for Duffing Equation

Abstract

Keywords

ASJC Scopus subject areas

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