Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Access Right: Closed AccessAuthor: search.filters.author.Tanoğlu, Gamze

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  • Article
    Citation - WoS: 9
    Citation - Scopus: 8
    A Numerical Method Based on Legendre Wavelet and Quasilinearization Technique for Fractional Lane-Emden Type Equations
    (Springer, 2023) İdiz, Fatih; Tanoğlu, Gamze; Aghazadeh, Nasser
    In 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: 10
    Citation - Scopus: 12
    An Efficient Approach for Solving Nonlinear Multidimensional Schrodinger Equations
    (Elsevier, 2021) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Tanoğlu, Gamze; Aziz, Imran; Siraj-ul-Islam
    An 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.