Mathematics / Matematik

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

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Author: search.filters.author.Korkut, Sıla ÖvgüCOAR Access Rights: search.filters.coarAccessRights.embargoed access

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  • Article
    A Reliable and Fast Mesh-Free Solver for the Telegraph Equation
    (Springer, 2022) İmamoğlu Karabaş, Neslişah; Korkut, Sıla Övgü; Gürarslan, Gürhan; Tanoğlu, Gamze
    In 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: 2
    Citation - Scopus: 3
    A Reliable Explicit Method To Approximate the General Type of the Kdv–burgers’ Equation
    (Springer, 2022) Korkut, Sıla Övgü; İmamoğlu Karabaş, Neslişah
    This study aims to propose a reliable, accurate, and efficient numerical approximation for a general compelling partial differential equation including nonlinearity (uδ∂u∂x), dissipation (∂2u∂x2), and dispersion (∂3u∂x3) which arises in many fields of engineering as well as applied sciences. The novel proposed method has been developed combining a kind of mesh-free method called the Taylor wavelet method with the Euler method. The convergence result of the method has been presented theoretically. Moreover, the validation and applicability of the method have been also confirmed computationally on benchmark problems such as KdV–Burgers’ equation and modified-KdV equation. The numerical results have been compared both to the exact solution and to those in the existing literature. All presented figures and tables guarantee that the proposed method is highly accurate, efficient, and compatible with the nature of the specified equation physically. Furthermore, the recorded errors are evidence that the proposed method is the best approximation compared to those in the existing methods.