Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/45
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Article Citation - Scopus: 25A Cubic B-Spline Galerkin Approach for the Numerical Simulation of the GEW Equation(International Academic Press, 2016) Karakoç, Seydi Battal Gazi; Zeybek, Halil; AGÜ; Zeybek, Halil; 01. Abdullah Gül UniversityThe generalized equal width (GEW) wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods. © 2016 Elsevier B.V., All rights reserved.Article A New Approach for Numerical Solution of Linear and Non-Linear Systems(Korean Soc Computational & Applied Mathematics & Korean Sigcam, 2017) Zeybek, Halil; Dolapci, Ihsan Timucin; AGÜ; Zeybek, Halil; 01. Abdullah Gül UniversityIn this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.Article Citation - Scopus: 31Numerical Solutions of the Kawahara Equation by the Septic B-Spline Collocation Method(International Academic Press, 2014) Karakoç, Seydi Battal Gazi; Zeybek, Halil; Ak, Turgut; AGÜ; Zeybek, Halil; 01. Abdullah Gül UniversityIn this article, a numerical solution of the Kawahara equation is presented by septic B-spline collocation method. Applying the Von-Neumann stability analysis, the present method is shown to be unconditionally stable. The accuracy of the proposed method is checked by two test problems. L2 and L∞ error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results. © 2016 Elsevier B.V., All rights reserved.Article Positive Solutions of Multipoint Φ-Laplacian BVPS With First-Order Derivative Dependence(World Scientific, 2023) Bachouche, Kamal; Tair, Hocine; Doǧan, Abdülkadir Muhittin; 0000-0002-3195-4718 View this author’s ORCID profile; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Doğan, Abdülkadir; 01. Abdullah Gül University; 02.01. Mühendislik Bilimleri; 02. Mühendislik FakültesiThis paper concerns existence of positive solutions for a second-order boundary value problem of Sturm-Liouville type associated with a φ-Laplacian operator and posed on a bounded interval. Existence results are obtained by an adapted version of the Krasnosel'skii's fixed point theorem of cone expansion and compression. Some examples illustrate our results. © 2023 Elsevier B.V., All rights reserved.
