WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7150
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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 - WoS: 4Citation - Scopus: 7On the Numerical Solution of Korteweg-De Vries Equation by the Iterative Splitting Method(Elsevier Ltd., 2011) Gücüyenen, Nurcan; Tanoğlu, GamzeIn this paper, we apply the method of iterative operator splitting on the Korteweg-de Vries (KdV) equation. The method is based on first, splitting the complex problem into simpler sub-problems. Then each sub-equation is combined with iterative schemes and solved with suitable integrators. Von Neumann analysis is performed to achieve stability criteria for the proposed method applied to the KdV equation. The numerical results obtained by iterative splitting method for various initial conditions are compared with the exact solutions. It is seen that they are in a good agreement with each other. © 2011 Elsevier Inc. All rights reserved.