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: 5Citation - Scopus: 5Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting(TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, GamzeIn this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.Article Citation - WoS: 2Citation - Scopus: 4An Efficient Iterative Algorithm for Solving Non-Linear Oscillation Problems(Faculty of Sciences and Mathematics, University of Nis, 2017) Korkut Uysal, Sıla Övgü; Tanoğlu, GamzeA 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, stability and order. Both the ϕ-functions and semigroup properties are used to overcome the presence of unboundedness of the operator. In order to confirm the theoretical results, the method is applied to three benchmark problems from the literature. The numerical results are compared with traditional splitting methods and confirm that the proposed method is more accurate as well as more efficient than the traditional splitting methods.Article Citation - Scopus: 13Convergence of Regional Economic Cycles in Turkey(John Wiley and Sons Inc., 2013) Duran, Hasan EnginDissimilar economic fluctuations and asymmetric shocks across the regions of a country might create severe policy distortions that, under these circumstances, aggregate policy interventions (such as taxation and interest rates), are likely to be sub-optimal for at least a fraction of the regions. For instance, monetary policy can hardly satisfy the needs of all regions when some of the regions are experiencing a boom while others are in a recession phase. For these reasons, similarity of regional business cycles and their convergence are highly desirable from a policy viewpoint. The aim of this paper is, therefore, to provide empirical evidence and policy implications in that context. In particular, I analyze business cycle correlations across Turkish provinces and the tendency of these cycles to converge over the period of analysis between 1975-2000 and 2004-2008 (for Nomenclature of Territorial Units for Statistics [NUTS]-2 regions). I find that regional business cycle asymmetries have tended to decrease in recent decades. This result, although it seems to provide evidence in favor of rising correlations, shows that the convergence process is rather slow and there still exist asymmetries across the regional business cycles.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.