Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

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Browsing Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science by Author "Anagnostopoulos, Antonios N."

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    B-Spline Method For Solving Bratu's Problem
    (Taylor & Francis Ltd, 4 Park Square, Milton Park, Abingdon Ox14 4Rn, Oxon, England, 2010) Valaristos, Antonios; Anagnostopoulos, Antonios N.; ÇAĞLAR, SÜLEYMAN HİKMET; ÇAĞLAR, HATİCE NAZAN; ÖZER, MEHMET; TR114368; TR110809; TR2509
    In this paper, we propose a B-spline method for solving the one-dimensional Bratu's problem. The numerical approximations to the exact solution are computed and then compared with other existing methods. The effectiveness and accuracy of the B-spline method is verified for different values of the parameter, below its critical value, where two solutions occur.
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    Dynamics of the solution of Bratu's equation
    (PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND, 2009-12-15) Çağlar, Hikmet; Çağlar, Nazan; Özer, Mehmet; Valaristos, Antonios; Miliou, Amalia N.; Anagnostopoulos, Antonios N.; TR114368; TR110809; TR2509
    In the present report we examine the dynamics exhibited by the solution of Bratu's equation. It represents a one-dimensional map with control parameter theta. For certain values of the parameter theta it exhibits successive bifurcations and shows chaotic regimes. This behaviour was confirmed by calculating the corresponding Lyapunov exponent, power spectra and cobweb diagrams, indicating similarities with other well-known one-dimensional maps. (C) 2008 Elsevier Ltd. All rights reserved.