Browsing by Author "Tanoğlu, Gamze"
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Analysis of a corner layer problem in anisotropic interfaces
Alikakos, N. D.; Bates, P. W.; Cahn, J. W.; Fife, P. C.; Fusco, G.; Tanoğlu, Gamze (Southwest Missouri State University, 200603)We investigate a model of anisotropic diffuse interfaces in ordered FCC crystals introduced recently by Braun et al and Tanoglu et al [3, 18, 19], focusing on parametric conditions which give extreme anisotropy. For a ... 
An application of the finite differences method to a dynamical interface problem
Ağıroğlu, İzzet Onur (İzmir Institute of Technology, 2004)A multipleorderparameter model for CuAu system on a face cubic centered lattice was recently developed in the presence of anisotropy. In that model, three order parameters (nonconserved) and one concentration order ... 
CMMSEconvergence analysis for operator splitting methods with application to BurgersHuxley equation
Çiçek, Yeşim; Tanoğlu, Gamze (Natural Sciences Publishing Corporation, 2015)We provide an error analysis of the operator splitting method of the LieTrotter type applied to the BurgersHuxley equation ut + αuux  εuxx = β(1  u)(u  γ)u. We show that the LieTrotter splitting method converges with ... 
Comparison of geometric integrator methods for Hamilton systems
İneci, Pınar (İzmir Institute of Technology, 2009)Geometric numerical integration is relatively new area of numerical analysis The aim of a series numerical methods is to preserve some geometric properties of the flow of a differential equation such as symplecticity or ... 
Convergence analysis and numerical solutions of the Fisher's and BenjaminBonoMahony equations by operator splitting method
Zürnacı, Fatma (İzmir 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
Çiçek, Yeşim (İzmir 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 ... 
The convergence of a new symmetric iterative splitting method for nonautonomous systems
Tanoğlu, Gamze; Korkut, Sıla (Taylor & Francis, 201209)The iterative splitting methods have been extensively applied to solve complicated systems of differential equations. In this process, we split the complex problem into several subproblems, each of which can be solved ... 
An efficient iterative algorithm for solving nonlinear oscillation problems
Korkut Uysal, Sıla Övgü; Tanoğlu, Gamze (Faculty of Sciences and Mathematics, University of Nis, 2017)A new iterative method is presented for numerical solution of nonlinear evolutionary problems. The convergence properties of the proposed method are analysed in abstract framework by using the concepts of consistency, ... 
Exact solution of some nonlinear differential equations by Hirota method
Güçoğlu, Deniz Hasan (İzmir 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 ... 
Finite element based stabilized methods for time dependent convectiondiffusion equation and their analysis
Yılmaz, Kemal Cem (İzmir 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 ... 
Higher order operator splitting methods via Zassenhaus product formula: Theory and applications
Geiser, Jürgen; Tanoğlu, Gamze; Gücüyenen, Nuran (Elsevier, 201108)In this paper, we contribute higher order operator splitting methods improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order ... 
Higher order symplectic methods based on modified vector fieldes
Demir, Duygu (İzmir Institute of Technology, 2009)The higher order, structure preserving numerical integrators based on the modified vector fields are used to construct discretizations of separable systems. This new approach is called as modifying integrators. Modified ... 
Higher order symplectic methods for separable Hamiltonian equations master of science
Gündüz, Hakan (İzmir Institute of Technology, 2010)The higher order, geometric structure preserving numerical integrators based on the modified vector fields are used to construct discretizations of separable Hamiltonian systems. This new approach is called as modifying ... 
Iterative operator splitting method for capillary formation model in tumor angiogenesis problem: Analysis and application
Gücüyenen, Nurcan; Tanoğlu, Gamze (WileyBlackwell, 201111)Iterative operator splitting method is used to solve numerically the mathematical model for capillary formation in tumor angiogenesis problem. The method is based on first splitting the complex problem into simpler ... 
New approaches for solving nonlinear oscillation problems
Korkut Uysal, Sıla Övgü (İzmir Institute of Technology, 201506)This thesis proposes two different numerical methods for solving nonlinear oscillation problems which appear in engineering and physics. Thus, the study is conducted in two parts. The first part introduces and analyzes ... 
Numerical solution of highly oscillatory differential equations by Magnus Series Method
Kanat, Bengi (İzmir Institute of Technology, 2006)In this study, the differential equation known as Lietype equation where the solutions of the equation stay in the LieGroup is considered. The solution of this equation can be represented as an infinite series whose terms ... 
Numerical solutions of the reactiondiffusion equations by exponential integrators
Sofyalıoğlu, Melek (İzmir Institute of Technology, 2014)This thesis presents the methods for solving stiff differential equations and the convergency analysis of exponential integrators, namely the exponential Euler method, exponential second order method, exponential midpoint ... 
On the numerical solution of Kortewegde Vries equation by the iterative splitting method
Gücüyenen, Nurcan; Tanoğlu, Gamze (Elsevier, 201110)In this paper, we apply the method of iterative operator splitting on the Kortewegde Vries (KdV) equation. The method is based on first, splitting the complex problem into simpler subproblems. Then each subequation is ... 
Operator splitting methhods for differential equations
Yazıcı, Yeşim (İzmir Institute of Technology, 2010)In this thesis, consistency and stability analysis of the traditional operator splitting methods are studied. We concentrate on how to improve the classical operator splitting methods via Zassenhaus product formula. In our ... 
Operator splitting method for parabolic partial differential equations: Analyses and applications
Gücüyenen, Nurcan (İzmir Institute of Technology, 2013)This thesis presents the consistency, stability and convergence analysis of an operator splitting method, namely the iterative operator splitting method, using various approaches for parabolic partial differential equations. ...