Mathematics / Matematik

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

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Language: search.filters.language.enSubject: search.filters.subject.Convergence analysis

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  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Convergence Analysis and Numerical Solution of the Benjamin-Bona Equation by Lie-Trotter Splitting
    (TUBITAK, 2018) Zürnacı, Fatma; Gücüyenen Kaymak, Nurcan; Seydaoğlu, Muaz; Tanoğlu, Gamze
    In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 4
    An Efficient Iterative Algorithm for Solving Non-Linear Oscillation Problems
    (Faculty of Sciences and Mathematics, University of Nis, 2017) Korkut Uysal, Sıla Övgü; Tanoğlu, Gamze
    A new iterative method is presented for numerical solution of nonlinear evolutionary problems. The convergence properties of the proposed method are analysed in abstract framework by using the concepts of consistency, stability and order. Both the ϕ-functions and semigroup properties are used to overcome the presence of unboundedness of the operator. In order to confirm the theoretical results, the method is applied to three benchmark problems from the literature. The numerical results are compared with traditional splitting methods and confirm that the proposed method is more accurate as well as more efficient than the traditional splitting methods.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    The Convergence of a New Symmetric Iterative Splitting Method for Non-Autonomous Systems
    (Taylor and Francis Ltd., 2012) Tanoğlu, Gamze; Korkut, Sıla
    The iterative splitting methods have been extensively applied to solve complicated systems of differential equations. In this process, we split the complex problem into several sub-problems, each of which can be solved sequentially. In this paper, we construct a new symmetric iterative splitting scheme based on the Magnus expansion for solving non-autonomous problems. We also study its convergence properties by using the concepts of stability, consistency, and order. Several numerical examples are illustrated to confirm the theoretical results by comparing frequently used methods. © 2012 Copyright Taylor and Francis Group, LLC.