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    Fibonacci Collocation Method for Solving a Class of Nonlinear Differential Equations
    (2023) Çakmak, Musa; Alkan, Sertan
    In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.
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    Fibonacci Collocation Method for Solving a Class of Nonlinear Differential Equations
    (Association of Mathematicians (MATDER), 2023) Çakmak, Musa; Alkan, Sertan
    In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature. © MatDer.
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    Fibonacci operational matrix algorithm for solving differential equations of Lane-Emden type
    (Sakarya Üniversitesi, 2019) Çakmak, Musa
    The aim of this study is to provide an effective and accurate technique for solving differential equations of Lane-Emden type as initial value problems. In this study, a numerical method called Fibonacci polynomial approximation method (FPAM) establish for approximate solution of Lane-Emden type differential equations by using Fibonacci polynomials. A matrix equation can be solved depending on the reduced form of the Lane-Emden type differential equations, which is characterized by an algebraic equation system, with the matrix relations of Fibonacci polynomials and their derivatives and their unknown Fibonacci coefficients. In addition, numerical results are given by comparisons to confirm the reliability of the proposed method for Lane-Emden type differential equations.
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    Hausdorff uzayların h-kapalı ve minimal hausdorff genişlemeleri
    (Hatay Mustafa Kemal Üniversitesi, 2011) Çakmak, Musa; Bilgin, Fevzi
    Bu çalışmada kompact uzayların genellemesi olan H-kapalı ve minimal hausdorff uzayları tanıtılacaktır. Tanım gereği bu uzaylar hausdorff uzaylarıdır. Bilindiği gibi compact hausdorff uzaylar tamamen regülerdir. O halde hausdorff uzayın compact hausdorff olabilmesi için kendisinin tamamen regüler olması gerekir. Bu çalışmada sadece Hausdorf olan bir uzayı yoğun bir biçimde içeren H-kapalı ve minimal hausdorff uzayların nasıl inşa edildiğini gösteren bir derleme verecektir.