Department department "Izmir Institute of Technology. Mathematics" and
Now showing items 2140 of 113

Computation of the convection diffusion equation by the fourth order compact finite difference method
(Izmir Institute of Technology, 2015)This dissertation aims to develop various numerical techniques for solving the one dimensional convection–diffusion equation with constant coefficient. These techniques are based on the explicit finite difference approximations ... 
Confinitely amply weakly supplemented modules
(Izmir Institute of Technology, 2005)We study amply weak supplemented modules and co¯nitely amply weakly supplemented modules in this thesis. We prove that every factor module, homomorphic image, supplemented submodule of an amply (co¯nitely) weak supplemented ... 
Convergence analysis and numerical solution of the BenjaminBonaMahony equation by LieTrotter splitting
(TUBITAK, 2018)In this paper, an operator splitting method is used to analyze nonlinear BenjaminBonaMahonytype equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then LieTrotter splitting ... 
Convergence analysis and numerical solutions of the Fisher's and BenjaminBonoMahony equations by operator splitting method
(Izmir Institute of Technology, 2014)This thesis is concerned with the operator splitting method for the Fisher’s and BenjaminBonoMahony type equations. We showthat the correct convergence rates inHs(R) space for Lie Trotter and Strang splitting method ... 
Convergence analysis of operator splitting methods for the BurgersHuxley equation
(Izmir Institute of Technology, 201507)The purpose of this thesis is to investigate the implementation of the two operator splitting methods; LieTrotter splitting and Strang splitting method applied to the Burgers Huxley equation and prove their convergence ... 
Damping oscillatory models in general theory of relativity
(Izmir Institute of Technology, 2007)In my thesis we have studied the universe models as dynamical systems which can be represented by harmonic oscillators. For example, a harmonic oscillatior equation is constructed by the transformation of the Riccati ... 
The Dirichlet problem for the fractional Laplacian
(Izmir Institute of Technology, 201712)This thesis is an introduction to the fractional Sobolev spaces and the fractional Laplace operator. We define the fractional Sobolev spaces and give their properties by comparing them with the classical version of Sobolev ... 
Discrete fractional integral operators and their relations to number theory
(Izmir Institute of Technology, 201807)The aim of this thesis is to get estimates on discrete fractional integral operators by using number theory. These operators, starting with the studies of Arkipov and Oskolkov, have been investigated for a long time. ... 
Dynamical systems on time scales
(Izmir Institute of Technology, 2007)In this thesis, we have studied dynamical systems on time scales. Firstly, we give basic definitions and theorems about the time scales and dynamical systems. We present Floquet theory and stability criterion on periodic ... 
Edge coloring of a graph
(Izmir Institute of Technology, 2004)The edge coloring problem is one of the fundamental problem on graphs which often appears in various scheduling problems like the le transfer problem on computer networks. In this thesis, we survey old and new results on ... 
Enriched finite elements method for convevtiondiffusionreaction problems
(Izmir Institute of Technology, 2012)In this thesis, we consider stabilization techniques for linear convectiondiffusionreaction (CDR) problems. The survey begins with two stabilization techniques: streamline upwind PetrovGalerkin method (SUPG) and Residualfree ... 
Entanglemend and topological soliton structures in Heisenberg spin models
(Izmir Institute of Technology, 2010)Quantum entanglement and topological soliton characteristics of spin models are studied. By identifying spin states with qubits as a unit of quantum information, quantum information characteristic as entanglement is ... 
Exact solution of some nonlinear differential equations by Hirota method
(Izmir Institute of Technology, 2005)The Hirota Bilinear Method is applied to construct exact analytical one solitary wave solutions of some class of nonlinear differential equations. first one the system of multidimensional nonlinear wave equation with the ... 
Exactly solvab qextended nonlinear classical and quantum models
(Izmir Institute of Technology, 2011)In the present thesis we study qextended exactly solvable nonlinear classical and quantum models. In these models the derivative operator is replaced by qderivative, in the form of finite difference dilatation operator. ... 
Exactly solvable generalized quantum harmonic oscillators related with the classical orthogonal polynomials
(Izmir Institute of Technology, 201607)In this thesis, we study exactly solvable generalized parametric oscillators related with the classical orthogonal polynomials of Hermite, Laguerre and Jacobi type. These quantum models with specific damping term, frequency ... 
Finite element based stabilized methods for time dependent convectiondiffusion equation and their analysis
(Izmir Institute of Technology, 201612)This study is focused on a Fourier stability and accuracy analysis of the time integration algorithms using generalized trapezioidal family of methods of scalar unsteady convection–diffusion equation with periodic boundary ... 
Fourier analysis on the Lorentz group and relativistic quantum mechanics
(Izmir Institute of Technology, 2008)The nonrelativistic Schrödinger and LippmanSchwinger equations are described. The expressions of these equations are investigated in momentum and configuration spaces, using Fourier transformation. The plane wave, which ... 
Generalization of cofinitely supplemented modules to lattices
(Izmir Institute of Technology, 2005)In this thesis we study how to extend the notion of co¯nitely supplemented module to lattice theory. A submodule N of a module M is called co¯nite if the factor module M/N is ¯nitely generated and we say that M is a co¯nitely ... 
Generalized GoldenFibonacci calculus and applications
(Izmir Institute of Technology, 201807)In the present thesis the GoldenFibonacci calculus is developed and several applications of this calculus are obtained. The calculus is based on the Golden derivative as a finite difference operator with Golden and Silver ...