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: 9Citation - Scopus: 8A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations(Springer, 2023) İdiz, Fatih; Tanoğlu, Gamze; Aghazadeh, NasserIn this research, we study the numerical solution of fractional Lane-Emden type equations, which emerge mainly in astrophysics applications. We propose a numerical approach making use of Legendre wavelets and the quasilinearization technique. The nonlinear term in fractional Lane-Emden type equations is iteratively linearized using the quasilinearization technique. The linearized equations are then solved using the Legendre wavelet collocation method. The proposed method is quite effective to overcome the singularity in fractional Lane-Emden type equations. Convergence and error analysis of the proposed method are given. We solve some test problems to compare the effectiveness of the proposed method with some other numerical methods in the literature.Article Citation - WoS: 10Citation - Scopus: 12An Efficient Approach for Solving Nonlinear Multidimensional Schrodinger Equations(Elsevier, 2021) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-IslamAn efficient numerical method is proposed for the solution of the nonlinear cubic Schrodinger equation. The proposed method is based on the Frechet derivative and the meshless method with radial basis functions. An important characteristic of the method is that it can be extended from one-dimensional problems to multi-dimensional ones easily. By using the Frechet derivative and Newton-Raphson technique, the nonlinear equation is converted into a set of linear algebraic equations which are solved iteratively. Numerical examples reveal that the proposed method is efficient and reliable with respect to the accuracy and stability.Article Citation - WoS: 8Operator-Splitting Methods Via the Zassenhaus Product Formula(Elsevier Ltd., 2011) Geiser, Juergen; Tanoğlu, GamzeIn this paper, we contribute an operator-splitting method improved by the Zassenhaus product. Zassenhaus products are of fundamental importance for the theory of Lie groups and Lie algebras. While their applications in physics and physical chemistry are important, novel applications in CFD (computational fluid dynamics) arose based on the fact that their sparse matrices can be seen as generators of an underlying Lie algebra. We apply this to classical splitting and the novel Zassenhaus product formula. The underlying analysis for obtaining higher order operator-splitting methods based on the Zassenhaus product is presented. The benefits of dealing with sparse matrices, given by spatial discretization of the underlying partial differential equations, are due to the fact that the higher order commutators are very quickly computable (their matrix structures thin out and become nilpotent). When applying these methods to convection-diffusion-reaction equations, the benefits of balancing time and spatial scales can be used to accelerate these methods and take into account these sparse matrix structures. The verification of the improved splitting methods is done with numerical examples. Finally, we conclude with higher order operator-splitting methods. (C) 2010 Elsevier Inc. All rights reserved.