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Öğe Application of cubic B-spline finite element technique to the thermistor problem(Elsevier Science Inc, 2004) Bahadir, ARA numerical solution to the thermistor problem is obtained using the cubic B-spline finite elements. The resulting system of ordinary differential equations is solved by the finite-difference method. Excellent agreement is obtained between the numerical results and the analytic solution for the three phases. (C) 2003 Elsevier Inc. All rights reserved.Öğe Exponential finite-difference method applied to Korteweg-de Vries equation for small times(Elsevier Science Inc, 2005) Bahadir, ARThe Korteweg-de Vries equation is numerically solved by using the exponential finite-difference technique. The accuracy of computed solutions is examined by comparison with Other numerical and analytical Solutions using two examples. The close results agreement between the Current results and the exact solutions confirms that the proposed finite-difference procedure is an effective technique for the solution of the Korteweg-de Vries equation at the small times. (C) 2003 Elsevier Inc. All rights reserved.Öğe A fully implicit finite-difference scheme for two-dimensional Burgers' equations(Elsevier Science Inc, 2003) Bahadir, ARThe two-dimensional Burgers' equations are discretized in fully implicit finite-difference form. This scheme leads to a system of nonlinear difference equations to be solved at each time-step. Newton's method is used to solve this nonlinear system. The linear system is solved by a direct method at each iteration of Newton's method. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. The present method performs well. (C) 2002 Published by Elsevier Science Inc.Öğe The investigation of the transient regimes in the nonlinear systems by the generalized classical method(Hindawi Publishing Corporation, 2005) Abbasov, T; Bahadir, ARThis paper presents the use of the generalized classical method (GCM) for solving linear and nonlinear differential equations. This method is based on the differential transformation (DT) technique. In the GCM, the solution of the nonlinear transient regimes in the physical processes can be written as a functional series with unknown coefficients. The series can be chosen to satisfy the initial and boundary conditions which represent the properties of the physical process. The unknown coefficients of the series are determined from the differential transformation of the nonlinear differential equation of the system. Therefore, the approximate solution of the nonlinear differential equation can be obtained as a closed-form series. The validity and efficiency of the GCM is shown using some transient regime problems in the electromechanics processes. The numerical results obtained by the present method are compared with the analytical solutions of the equations. It is shown that the results are found to be in good agreement with each other.Öğe Magnetoimpedance effect in electrochemically etched CoFeSiB amorphous wires(Elsevier Science Bv, 2005) Atalay, FE; Atalay, S; Kaya, H; Bahadir, ARAs-received CoFeSiB amorphous wires with 128 mu m diameter were electrochemically etched at constant voltage to obtain micro magnetoimpedance (MI) sensor. Wires with different diameters from 13 to 100 mu m were obtained at various constant voltage and pH conditions. The diameters and surface properties of the wires were studied by scanning electron microscopy. It was found that the magnitude of the magnetoimpedance effect was first increased and then decreased with decreasing wire diameter. The thinnest wire obtained at pH 4 and 0.4 V, has a diameter of 13 mu m and this wire shows a 4.95% variation in the magnitude of (Delta Z/Z)(%). The results were discussed On the basis of internal stress distribution and a simple magnetic moment rotational model. (c) 2005 Elsevier B.V. All rights reserved.Öğe A mixed finite difference and boundary element approach to one-dimensional Burgers' equation(Elsevier Science Inc, 2005) Bahadir, AR; Saglam, MThis paper presents a mixed method for the numerical solution of the one-dimensional Burgers' equation. This method Uses mixed boundary elements in association with finite differences. Two standard problems are used to validated the algorithm. Comparisons are made with some of the existing numerical schemes and analytical solutions. The proposed method performs well. (C) 2003 Elsevier Inc. All rights reserved.Öğe A numerical investigation of the liquid flow velocity over an infinity plate which is taking place in a magnetic field(Ios Press, 2005) Bahadir, AR; Abbasov, TIn this paper the change of the magnetchydrodynamic flow velocity of the infinite plate in the non stationary motion of the incompressible viscous liquid has been studied numerically. Outer magnetic field has been directed perpendicular to the plate and assumed moving with the plate. For the different dynamical motion of the plate, the evolution of the velocity has been investigated numerically. The magnetic field induction and the changing of the parameters of the dynamical system on a large range effect to the velocity has been investigated. At a specific point increasing of the magnetic field induction causes decreasing in the velocity. By the increasing the parameters of the manyetohydrodinamic system, the problem becomes more difficult to solve analytically. Therefore, a numerical solution technique is resorted to solve the problem approximately.Öğe Numerical solution of one-dimensional Burgers equation(Elsevier Science Bv, 1999) Kutluay, S; Bahadir, AR; Özdes, AThis 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.Öğe The numerical solution of one-phase classical Stefan problem(Elsevier Science Bv, 1997) Kutluay, S; Bahadir, AR; Ozdes, AIn this paper, variable space grid and boundary Immobilisation Techniques based on the explicit finite difference are applied to the one-phase classical Stefan problem. It is shown that all the results obtained by the two methods are in good agreement with the exact solution, and exhibit the expected convergence as the mesh size is refined.Öğe On the performance of certain direct and iterative methods on equations arising on a two-dimensional in situ combustion simulator(Elsevier Science Inc, 2002) Bahadir, AR; Ellerby, FBA two-dimensional mathematical model of the in situ combustion process involves a set of nonlinear partial differential equations. These equations are discretized in implicit finite-difference form. The resulting set of nonlinear algebraic equations are solved for each time-step by use of a Newton-Raphson procedure. Each Newton iteration produces an equation of the form Ax = b, (*) where x is the Newton update, b is the current residual of the nonlinear equations and A is the Jacobian matrix. A is lar-e and has a non-symmetric, sparse structure. In this current work we wish to compare the performance of LU factorization, ORTHO-MIN(m) and more recent iterative methods, GMRES(m) and BI-CGSTAB to solve (*) on the model of the in situ combustion problem. To increase the convergence rate for the iterative methods a preconditioning and a scaling technique are used. (C) 2002 Elsevier Science Inc. All rights reserved.Öğe A small time solutions for the Korteweg-de Vries equation(Elsevier Science Inc, 2000) Kutluay, S; Bahadir, AR; Özdes, AIn 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.Öğe Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method(Hindawi Ltd, 2002) Bahadir, ARThe problem of heat transfer in a Positive Temperature Coefficient (PTC) thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.Öğe Surprising magnetic behavior of cobalt(II) ion in recently prepared macrocycle complexes.: Distortion versus intermolecular antiferromagnetic exchange interactions(Springer, 2005) Bayri, A; Bahadir, AR; Avcu, FM; Aytekin, ÖThe magnetic moment of the Co2+ stop ion in the newly reported macrocycle complex is analysed for various situations. It is realized that in order to obtain the observed magnetic moment, either some irrelevant parameters or some intermolecular antiferromagnetic interactions must be included in the magnetic Hamiltonian. It is suggested that the complex behaves as a largely distorted octahedron.Öğe Torsional stress impedance effect in Fe71Cr7Si9B13 amorphous wire(Wiley-V C H Verlag Gmbh, 2004) Atalay, FE; Bayri, N; Bahadir, AR; Atalay, SThe magnetoimpedance effect has been measured in as-received and current annealed Fe71Cr7Si9B13 amorphous wires under torsional stress varied up to 1.2 rad/cm. It was found that the torsional stress dependence of impedance of as-received amorphous wire has a non-monotonous shape with first an increase of the impedance and then a decrease. On the other hand, the impedance of current annealed wire directly starts to decrease with increasing torsional stress. The current annealing of wire results in a large variation in the magnitude of torsional stress impedance effect, (DeltaZ/Z)xi(%), up to 150%. Also, a simple mathematical model based on the magnetic moment rotation to explain torsional stress versus impedance data was developed and the results were partly discussed on the basis of this model.Öğe A variety of finite difference methods to the thermistor with a new modified electrical conductivity(Elsevier Science Inc, 1999) Kutluay, S; Bahadir, AR; Özdes, AWe 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.Öğe Various methods to the thermistor problem with a bulk electrical conductivity(Wiley, 1999) Kutluay, S; Bahadir, AR; Özdes, AIn 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.
