Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 4Citation - Scopus: 4A New Numerical Algorithm Based on Quintic B-Spline and Adaptive Time Integrator for Cou- Pled Burger's Equation(Tabriz University, 2023) Çiçek, Yeşim; Gücüyenen Kaymak, Nurcan; Bahar, Ersin; Gürarslan, Gürhan; Tanoğlu, GamzeIn this article, the coupled Burger's equation which is one of the known systems of the nonlinear parabolic partial differential equations is studied. The method presented here is based on a combination of the quintic B-spline and a high order time integration scheme known as adaptive Runge-Kutta method. First of all, the application of the new algorithm on the coupled Burger's equation is presented. Then, the convergence of the algorithm is studied in a theorem. Finally, to test the efficiency of the new method, coupled Burger's equations in literature are studied. We observed that the presented method has better accuracy and efficiency compared to the other methods in the literature. © 2023 University of Tabriz. All Rights Reserved.Article A Reliable and Fast Mesh-Free Solver for the Telegraph Equation(Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Gürarslan, Gürhan; Tanoğlu, GamzeIn the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature.Article Citation - WoS: 2Citation - Scopus: 2The Convergence of a New Symmetric Iterative Splitting Method for Non-Autonomous Systems(Taylor and Francis Ltd., 2012) Tanoğlu, Gamze; Korkut, SılaThe iterative splitting methods have been extensively applied to solve complicated systems of differential equations. In this process, we split the complex problem into several sub-problems, each of which can be solved sequentially. In this paper, we construct a new symmetric iterative splitting scheme based on the Magnus expansion for solving non-autonomous problems. We also study its convergence properties by using the concepts of stability, consistency, and order. Several numerical examples are illustrated to confirm the theoretical results by comparing frequently used methods. © 2012 Copyright Taylor and Francis Group, LLC.Article Citation - WoS: 16Citation - Scopus: 18Solitary Wave Solution of Nonlinear Multi-Dimensional Wave Equation by Bilinear Transformation Method(Elsevier Ltd., 2007) Tanoğlu, GamzeThe Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated.