TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4

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Author: search.filters.author.Sezer, MehmetSubject: search.filters.subject.Collocation Method

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  • Article
    Citation - WoS: 11
    Citation - Scopus: 11
    A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types
    (Scientific Technical Research Council Turkey-Tubitak, 2019-01-18) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
    In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 20
    Lucas Polynomial Solution of Nonlinear Differential Equations With Variable Delays
    (Hacettepe Univ, Fac Sci, 2020-04-02) Gumgum, Sevin; Savasaneril, Nurcan Baykus; Kürkçü, ÖmÜr Kıvanç; Sezer, Mehmet; Kürkҫü, Ömür Kıvanҫ
    In this study, a novel matrix method based on Lucas series and collocation points has been used to solve nonlinear differential equations with variable delays. The application of the method converts the nonlinear equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Lucas coefficients. The method is tested on three problems to show that it allows both analytical and approximate solutions.