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Mathematics / Matematik

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

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Browsing Mathematics / Matematik by Journal "Applied and Computational Mathematics"

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    Boundary Integral Equations for the Exterior Robin Problem in Two Dimensions
    (Elsevier, 2018-11) Ivanyshyn Yaman, Olha; Özdemir, Gazi; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    We propose two methods based on boundary integral equations for the numerical solution of the planar exterior Robin boundary value problem for the Laplacian in a multiply connected domain. The methods do not require any a-priori information on the logarithmic capacity. Investigating the properties of the integral operators and employing the Riesz theory we prove that the obtained boundary integral equations for both methods are uniquely solvable. The feasibility of the numerical methods is illustrated by examples obtained via solving the integral equations by the Nyström method based on weighted trigonometric quadratures on an equidistant mesh.
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    Structure and Stability of Bimodal Systems in R-3: Part 1
    (Azerbaijan National Academy of Sciences, 2014) Eldem, Vasfi; Şahan, Gökhan; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In this paper, the structure and global asymptotic stability of bimodal systems in R3 are investigated under a set of assumptions which simplify the geometric structure. It is basically shown that one of the assumptions being used reduces the stability problem in R3 to the stability problem in R2. However, structural analysis shows that the behavior of the trajectories changes radically upon the change of the parameters of individual subsystems. The approach taken is based on the classification of the trajectories of bimodal systems as i) the trajectories which change modes finite number of times as t ? ?, and ii) the trajectories which change modes infinite number of times as t ? ?. Finally, it is noted that this approach can be used without some of the assumptions for all bimodal systems in R3, and for bimodal systems in Rn. © 2014, Azerbaijan National Academy of Sciences. All rights reserved.