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Browsing Scopus by Department "Izmir Institute of Technology"

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    Journal Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Convergence analysis and numerical solution of the benjamin-bona-mahony equation by lie-trotter splitting
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Zurnaci, Fatma; Gucuyenen Kaymak, Nurcan; Seydaoglu, Muaz; Tanoglu, 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.
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    Journal Article
    Citation - WoS: 16
    Citation - Scopus: 18
    Solitary wave solution of nonlinear multi-dimensional wave equation by bilinear transformation method
    (Elsevier Science Bv, 2007) Tanoglu, Gamze
    The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated. (C) 2006 Published by Elsevier B.V.