الفهرس 
Historical BackgroundOnly 14 pages are availabe for public view
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Abstract
This thesis presents numerical simulation of some KdV type equation using Galerkin’s finite element method. Two examples showed in the thesis Extended KdV and Gardner-Extended KdV.
In 1834, Russell a scholar discovered an empirical equation describing the wave according to the speed of each wave depending on the depth of the undisturbed water and the maximum height of the wave above the level of the undisturbed water. After that, the two scientists Korteweg and de Vries developed the well-known KdV equation which is important to provide a scientific explanation of the phenomenon of solitary waves, or solitons, and they derived an equation describing the propagation of small amplitude and long waves on the surface of shallow water.
The Kortweg-de Vries (KdV) equation is a nonlinear partial differential equation of third order, we mentioned a few of KdV applications _elds, many of these applications are in fluid mechanics, which is not surprising given that this _eld continues to play a crucial role in physics as the one where many important nonlinear structures, such as shocks, solitons, and plasma.
The Kortweg-de Vries equations are simplest of mathematical models to contain the physical effects of these waves, nonlinear and dispersive wave interactions. The interest has been developed in the numerical treatment of partial differential equations describing non-linear wave phenomena so much in recent years. These equations are used to model nonlinear dispersive waves in a wide range of application areas, such as water wave models and plasma physics.
The main objectives of this thesis are to design a reliable, efficient accurate algorithm for solving KdV type equations and carrying out simulations to show the validity and reliability of these algorithms designed based on a Galerkin’s finite element method, quintic B-spline. This numerical method is then applied to Extended KdV equation and Gardner-Extended KdV equation. Time integration of the resulting systems is affected using Crank Nicholson approximation in time. Simulations including propagation of solitary waves and interaction of two solitary waves are studied and represented.