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 Publisher "Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 USA"

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    Coefficient inequality for q-starlike functions
    (Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 USA, 2016-03-05) Özkan Uçar, H. Esra
    Let A be the class of analytic functions f which are regular and satisfying the conditions f (0) = 0, f'(0) = 1. In other words each f in A has the power series representation f(z) = z + a(2)z(2) + a(3)z(3) + ... in the open unit disc D = {z parallel to z} < 1}. For every q is an element of (0, 1), let q-difference operator be defined as follows D(q)f(z) = f(z) - f(zq)/z(1-q) (z is an element of D) Making use of the above operator we define a class of analytic functions, so called q-close-to-convex function with respect to Janowski starlike functions and the class of such functions is defined by K-q(A, B). In the present paper we will study on this class. (C) 2015 Elsevier Inc. All rights reserved.
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    Model order reduction for nonlinear Schrodinger equation
    (Elsevier Science Inc, 360 Park Ave South, New York, Ny 10010-1710 USA, 2015-05-01) Karasözen, Bülent; Akkoyunlu, Canan; Uzunca, Murat; 1233; 113376; 163841
    We apply the proper orthogonal decomposition (POD) to the nonlinear Schrodinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving symplectic mid-point rule. A priori error estimates are derived for the POD reduced dynamical system. Numerical results for one and two dimensional NLS equations, coupled NLS equation with soliton solutions show that the low-dimensional approximations obtained by POD reproduce very well the characteristic dynamics of the system, such as preservation of energy and the solutions. (C) 2015 Elsevier Inc. All rights reserved.