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

<p>In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform. Here, we present a comparative study of the new technique based on Laplace transform and the previous techniques of maximum minimum approach (MMA) and amplitude frequency formulation (AFF) for the analytical results. For the non-linear oscillators, MMA, AFF and VIM by Laplace transform give the same analytical results. Comparison of analytical results of VIM by Laplace transform with numerical results by fourth-order Runge–Kutta (RK) method conforms the soundness of the method for solving non-linear oscillators as well as for the time and boundary conditions of the non-linear oscillators.</p>
</abstract>

In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform. Here, we present a comparative study of the new technique based on Laplace transform and the previous techniques of maximum minimum approach (MMA) and amplitude frequency formulation (AFF) for the analytical results. For the non-linear oscillators, MMA, AFF and VIM by Laplace transform give the same analytical results. Comparison of analytical results of VIM by Laplace transform with numerical results by fourth-order Runge–Kutta (RK) method conforms the soundness of the method for solving non-linear oscillators as well as for the time and boundary conditions of the non-linear oscillators.

Modified Laplace Based Variational Iteration Method for the Mechanical Vibrations and its Applications

Faculty of Physical Sciences, Department of Mathematics

Acta Mechanica et Automatica

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

In this paper, we are putting forward the periodic solution of non-linear oscillators by means of variational iterative method (VIM) using Laplace transform....

Modified Laplace Based Variational Iteration Method for the Mechanical Vibrations and its Applications

Published Online: Mar 16, 2022

Page range: 98 - 102

Received: Oct 25, 2021

Accepted: Jan 12, 2022

DOI: https://doi.org/10.2478/ama-2022-0012

Keywords
variational iterative method, non-linear oscillator, Laplace transform

© 2022 Shahida Rehman et al., published by Sciendo

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

Modified Laplace Based Variational Iteration Method for the Mechanical Vibrations and its Applications

Published Online: Mar 16, 2022

Page range: 98 - 102

Received: Oct 25, 2021

Accepted: Jan 12, 2022

DOI: https://doi.org/10.2478/ama-2022-0012

Keywordsvariational iterative method, non-linear oscillator, Laplace transform

© 2022 Shahida Rehman et al., published by Sciendo

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

Keywords
variational iterative method, non-linear oscillator, Laplace transform