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    A finite element approach for solution of Burgers' equation
    (Elsevier Science Inc, 2003) Özis, T; Aksan, EN; Özdes, A
    In this study, for the Burgers' equation which is used a model problem in turbulence and shock wave theory was given a finite element solution. Considering the numerical results obtained for different values of viscosity compared with Cole's analytical solution, it was seen that they were in good agreement. (C) 2002 Published by Elsevier Science Inc.
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    A numerical solution of Burgers' equation
    (Elsevier Science Inc, 2004) Aksan, EN; Özdes, A
    In this paper, the Burgers' equation which is one-dimensional quasi-linear parabolic partial differential equation was solved by a variational method constructed on the method of discretization in time. The numerical results obtained by these ways for various values of viscosity have been compared with the exact solution. It was seen that they were in good agreement with each other. (C) 2003 Elsevier Inc. All rights reserved.
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    Numerical solution of Korteweg-de Vries equation by Galerkin B-spline finite element method
    (Elsevier Science Inc, 2006) Aksan, EN; Özdes, A
    A finite element solution of the KdV equation is presented. To demonstrate the efficiency of the method two test problems are considered. The numerical solutions of the KdV equation are compared with both the exact solutions and other numerical solutions in the literature. The numerical solutions are found to be in good agreement with the exact solutions. (c) 2005 Elsevier Inc. All rights reserved.
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    Numerical solution of one-dimensional Burgers equation
    (Elsevier Science Bv, 1999) Kutluay, S; Bahadir, AR; Özdes, A
    This paper presents finite-difference solution and analytical solution of the finite-difference approximations based on the standard explicit method to the one-dimensional Burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics. Results obtained by these ways for some modest values of viscosity have been compared with the exact (Fourier) one. It is shown that they are in good agreement with each other. (C) 1999 Elsevier Science B.V. All rights reserved. AMS classification 65N06.
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    A small time solutions for the Korteweg-de Vries equation
    (Elsevier Science Inc, 2000) Kutluay, S; Bahadir, AR; Özdes, A
    In this paper a heat balance integral (HBI) method is applied to the one-dimensional non-linear Korteweg-deVries (KdV) equation prescribed by appropriate homogenous boundary conditions and a set of initial conditions to obtain its approximate analytical solutions at small times. It is shown that the HBI solutions obtained by the method may be used effectively at small times when the exact solution of the KdV equation is not known. (C) 2000 Elsevier Science Inc. All rights reserved.
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    Thermal conductivity properties of glass-ceramic (Bi2-?-?Ga?Tl?)Sr2Ca2Cu3O10+x high-Tc superconductors
    (Kluwer Academic/Plenum Publ, 1999) Balci, Y; Yakinci, ME; Aksan, MA; Özdes, A; Ates, H
    Glass-ceramic BSCCO superconductors with nominal (Bi2-delta-gammaGadeltaTlgamma)Sr2Ca2Cu3O10+x compositions, where delta=0.20, 0.40, 0.60 and gamma=0.10, 0.30, 0.40, have been prepared by the melt quenching method. The thermal conductivity, kappa(T) measurements were performed between 30K and 285K and results obtained found to be between 3.1 and 9.9 mW/cm.K depending an the substitution levels and temperature. Results obtained showed that the phonon-defect scattering dominates above the T-c for all samples but below the T-c a strong coupling mechanism occurs. The best electrical performance was obtained to be 113K and 107K for T-c and T-zero, respectively.
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    A variational approximation to the problem of the deflection of a bar
    (Elsevier Science Inc, 2004) Aksan, EN; Özdes, A; Esen, A
    In this paper, a mathematical modelling of the deflection of a bar lying on an elastic medium. It was shown that results obtained were reasonably in good agreement with Ritz solution. (C) 2003 Elsevier Inc. All rights reserved.
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    A variety of finite difference methods to the thermistor with a new modified electrical conductivity
    (Elsevier Science Inc, 1999) Kutluay, S; Bahadir, AR; Özdes, A
    We consider the numerical solution of a one-dimensional thermistor (thermo-electric) problem with a new modified step function electrical conductivity which is an inherently non-linear function of the temperature. A variety of finite difference methods are applied to solve the problem using a new modification of the step function electrical conductivity to be satisfied the physical phenomena of the problem. (C) 1999 Elsevier Science Inc. All rights reserved.
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    Various methods to the thermistor problem with a bulk electrical conductivity
    (Wiley, 1999) Kutluay, S; Bahadir, AR; Özdes, A
    In this paper, Explicit Finite Difference (EFD), Galerkin Finite Element (GFE) and Heat-Balance Integral (HBI) methods are applied to the one-dimensional thermistor problem with a bulk electrical conductivity to obtain its steady-state solutions. It is shown that EFD, GFE and HBI solutions exhibit the correct physical characteristic of the problem, and they are in very good agreement with the exact solution. The only marked difference is time to attain steady states. (C) 1999 John Wiley & Sons, Ltd.