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Browsing Mathematics / Matematik by Author "Tanoğlu, Gamze"
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A1L10 phase boundaries and anisotropy via multipleorderparameter theory for an fcc alloy
Tanoğlu, Gamze; Braun, Richard J.; Cahn, John W.; McFadden, Geoffrey B. (European Mathematical Society Publishing House, 2003)The dependence of thermodynamic properties of planar interphase boundaries (IPBs) and antiphase boundaries (APBs) in a binary alloy on an fcc lattice is studied as a function of their orientation. Using a recently developed ... 
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 ... 
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 ... 
A conserved linearization approach for solving nonlinear oscillation problems
Korkut, Sıla Övgü; Gücüyenen Kaymak, Nurcan; Tanoğlu, Gamze (Natural Sciences Publishing, 201805)Nonlinear oscillation problems are extensively used in engineering and applied sciences. Due to nonavailability of the analytic solutions, numerical approaches have been used for these equations. In this study, a numerical ... 
Convergence analysis and numerical solution of the BenjaminBonaMahony equation by LieTrotter splitting
Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, Gamze (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 ... 
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, ... 
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 ... 
The Hirota Method for reactiondiffusion equations with three distinct roots
Tanoğlu, Gamze; Pashaev, Oktay (AIP Publishing, 2004)The Hirota Method, with modified background is applied to construct exact analytical solutions of nonlinear reactiondiffusion equations of two types. The first equation has only nonlinear reaction part, while the second ... 
Hirota method for solving reactiondiffusion equations with generalized nonlinearity
Tanoğlu, Gamze (World Academic Press, 2006)The Hirota Method is applied to find an exact solitary wave solution to evolution equation with generalized nonlinearity. By introducing the power form of Hirota ansatz the bilinear representation for this equation is ... 
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 ... 
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 ... 
An operator splitting approximation combined with the supg method for transport equations with nonlinear reaction term
Baysal, Onur; Tanoğlu, Gamze (Tech Science Press, 2012)In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with nonlinear reaction term. We split the transport equation into a reaction part and an ... 
Solitary wave solution of nonlinear multidimensional wave equation by bilinear transformation method
Tanoğlu, Gamze (Elsevier, 200710)The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multidimensional nonlinear wave equation for ncomponent vector with modified background. The nonlinear part is the ... 
Strang splitting method for BurgersHuxley equation
Çiçek, Yeşim; Tanoğlu, Gamze (Elsevier, 20160305)We derive an analytical approach to the Strang splitting method for the BurgersHuxley equation (BHE) ut+αuuxε uXX=β(1u)(uγ)u. We proved that Srtang splitting method has a second order convergence in Hs(R), where Hs(R) ... 
Vector shock soliton and the Hirota bilinear method
Pashaev, Oktay; Tanoğlu, Gamze (Elsevier, 200510)The Hirota bilinear method is applied to find an exact shock soliton solution of the system reactiondiffusion equations for ncomponent vector order parameter, with the reaction part in form of the third order polynomial, ...