<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Modified Semi-Analytical Approach for Duffing Equation

Abdus Salam School of Mathematical Sciences

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Modified Semi-Analytical Approach for Duffing Equation"}

This research endeavour-investigates the enhanced adaptation of the Laplace-based variational iteration method (VIM) tailored specifically for tackling the...

Modified Semi-Analytical Approach for Duffing Equation

Publicado en línea: 26 jun 2024

Páginas: 300 - 306

Recibido: 04 jul 2023

Aceptado: 18 oct 2023

DOI: https://doi.org/10.2478/ama-2024-0033

Palabras clave
nonlinear dynamics, modified variational iterative method, Simulink model, mechanical vibration

© 2024 Um E Amara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Modified Semi-Analytical Approach for Duffing Equation

Publicado en línea: 26 jun 2024

Páginas: 300 - 306

Recibido: 04 jul 2023

Aceptado: 18 oct 2023

DOI: https://doi.org/10.2478/ama-2024-0033

Palabras clavenonlinear dynamics, modified variational iterative method, Simulink model, mechanical vibration

© 2024 Um E Amara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
nonlinear dynamics, modified variational iterative method, Simulink model, mechanical vibration