Solution of the van der pol oscillator equation by Laplace transform methods

Other Title(s)

حل معادلة متذبذب فان دربول باستخدام تحويلات لابلاس

Dissertant

al-Nawayisah, Jumanah Khalil

Thesis advisor

Jaradat, Imad Khalid Yusuf

Comitee Members

al-Wardat, Mashhur Ahmad Salamah
al-Uqayli, Amir Dakhil
al-Shar, Muhammad Abd al-Karim

University

Mutah University

Faculty

Faculty of Science

Department

Department of physics

University Country

Jordan

Degree

Master

Degree Date

2017

English Abstract

In this work , we studied Van der Pol Oscillator equation as an example of a nonlinear oscillator represented by second order differential equation.

First, we studied linear oscillators, and we applied Laplace Transforms and the boundary conditions to find the general solutions in the three cases of damping (critical damping,over damping and under damping),the results were plotted using mathmaticha 6.

Then we studied Van der Pol Oscillator as an example of a nonlinear oscillator, and we derivied it's equation.

Then by using Laplace Decomposition method we got approximate solution, which we plotted for different values of damping coefficient μ.

Then we found the exact sloution for fractional Van der Pol oscillator using fractional Laplace transform in the Caputo definition.

Acomparison between the classical solution and the fractional solution is presented by plotting their solutions using mathmaticha

Main Subjects

Physics

Topics

• Differential equations
• Statistical physics
• Laplace transformation

No. of Pages

86

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-749470