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Deanship of Graduate Studies
Document Details
Document Type
:
Thesis
Document Title
:
Numerical Solution of Coupled Nonlinear Shrödinger-KdV Equations
الحلول العددية لمعادلات Shrödinger-KdV المزدوجة غير الخطية
Subject
:
mathematics department
Document Language
:
Arabic
Abstract
:
The aim of this thesis is to solve numerically the coupled nonlinear Shrödinger -KdV equations using finite difference method. In chapter 1: We present in detail, this equation and the exact solution, also we study its conserved quantities. The solution of the block tridiagonal system and penta-diagonal system are derived. We describe the fixed point method and Runge Kutta of order 4 method for solving the nonlinear system. In chapter 2: We solve the coupled nonlinear Shrödinger -KdV equations numerically by using explicit method. The accuracy of the resulting scheme is second order in space and first order in time and conditionally stable. Also, we have used the explicit Runge Kutta of order 4 method where the accuracy of the resulting scheme is second order in space and forth order in time and it is conditionally stable. We give the some numerical examples to show that this method is conserving the conserved quantities. In chapter 3: We present another method for solving the coupled nonlinear Shrödinger-KdV equations using Crank-Nicolson method, we get a scheme which is second order in space and time, and conditionally stable. We use fixed point method for solving the nonlinear system obtained. We give some numerical examples to show that this method is conserving quantities. In chapter 4: We solve the coupled nonlinear Shrödinger -KdV equations numerically by linearizing the nonlinear system. Three linearization techniques are adopted. The accuracy of the resulting scheme in each case is second order in space and time and it is unconditionally stable. We give some numerical examples to show that this method is conserving the conserved quantities.
Supervisor
:
Dr. Mohammad Said Hammoudah
Thesis Type
:
Master Thesis
Publishing Year
:
1433 AH
2012 AD
Co-Supervisor
:
Dr. Farida M. Mosally
Added Date
:
Sunday, December 16, 2012
Researchers
Researcher Name (Arabic)
Researcher Name (English)
Researcher Type
Dr Grade
Email
خديجة محمد العمودي
Al-Amoudi, Khadijah Mohammed
Researcher
Master
Files
File Name
Type
Description
34758.pdf
pdf
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