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 TypeDr GradeEmail
خديجة محمد العموديAl-Amoudi, Khadijah MohammedResearcherMaster 

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