Solution for the nonlinear korteweg-de vries (KdV)‎ equation using Adomian polynomial

Other Title(s)

حل معادلة (Korteweg-de Vries)‎ اللاخطية باستخدام متعددة الحدود (Adomian)‎

Dissertant

al-Shubul, Ali Atif

Thesis advisor

Jaradat, Imad Khalid Yusuf

Comitee Members

al-Dumur, Hmud Abd al-Hamid
Abu Samak, Mahmud Khalid
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 the equation of linear harmonic oscillator and solve it using (Laplace Transform) (LT).

We then studied the damped oscillator in terms of its characteristics and solve its equation using (LT) by applying the initial conditions for obtaining the three states and then drawing the solutions of these types using the software (Mathematica 11).

We then studied the nonlinear equation and solved it using the (Laplace Adomian Decomposition Method) (LADM).

Then we studied the fractional calculus equation which is called (Caputo Fractional Derivative).

Then we began to study the (Korteweg de Vries) (KdV) equation in terms of its properties, its application and the formula of its equations in three types (General, fifth and seventh - order).

The main objective of this study is to solve the (KdV) equation by using the first methods (LADM) and the second method (Fractional Calculus).

Then we draw the solutions using the software (Mathematica 11).

Finally, we compared the results of the equation solution in both ways

Main Subjects

Physics

No. of Pages

59

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-779165