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    An analytical-numerical method for solving the Korteweg-de Vries equation
    (Elsevier Science Inc, 2005) Özer, S; Kutluay, S
    In this paper, an analytical-numerical method is applied to the one-dimensional Korteweg-de Vries equation with a variant of boundary and initial conditions to obtain its numerical solutions at small times. Two test problem with known exact solutions are studied to demonstrate the accuracy of the present method. The obtained results are compared with the exact solution of each problem and are found to be in good agreement with each other. The numerical scheme is also compared with earlier work and shown to be accurate and efficient. (c) 2004 Elsevier Inc. All rights reserved.
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    Application of a lumped Galerkin method to the regularized long wave equation
    (Elsevier Science Inc, 2006) Esen, A; Kutluay, S
    In this paper, a lumped Galerkin method based on quadratic B-spline finite elements is used to find numerical solutions of the one-dimensional regularized long wave (RLW) equation with a variant of initial and boundary conditions. The obtained numerical results show that the present method is a remarkably Successful numerical technique for solving the equation. Results are compared with published numerical solutions. A linear stability analysis of the scheme is also investigated. (c) 2005 Elsevier Inc. All rights reserved.
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    A B-spline finite element method for the thermistor problem with the modified electrical conductivity
    (Elsevier Science Inc, 2004) Kutluay, S; Esen, A
    In this paper, approximate steady-state solutions of a one-dimensional positive temperature coefficient thermistor problem with a modified step function electrical conductivity are obtained by using the Galerkin cubic B-spline finite element method. It is shown that the computational results obtained by the method display the correct physical characteristics of the problem, and they are found to be in very good agreement with the exact solution. It is also shown that the numerical solution exhibits the expected convergence to the exact one as the mesh size is refined. Further a Fourier stability analysis of the method is investigated. (C) 2003 Elsevier Inc. All rights reserved.
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    Finite element approaches to the PTC thermistor problem
    (Elsevier Science Inc, 2005) Kutluay, S; Esen, A
    In this paper, subdomain collocation (SC) and Petrov-Galerkin (PG) methods based on spline finite elements have been applied to the one-dimensional positive temperature coefficient (PTC) thermistor problem with a temperature dependent ramp function electrical conductivity to obtain the predicted temperature distributions and the locations of the free boundaries in the steady-state case. The numerical results obtained by the present methods have been compared with the exact solution and also those obtained by earlier authors. A Fourier stability analysis of each method is investigated. (C) 2004 Elsevier Inc. All rights reserved.
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    Finite element solution of the thermistor problem with a ramp electrical conductivity
    (Elsevier Science Inc, 2005) Kutluay, S; Esen, A
    This paper presents approximate steady-state solutions of a one-dimensional positive temperature coefficient thermistor problem with a ramp function electrical conductivity using the Galerkin cubic B-spline finite element method. The numerical results obtained by the present method have been compared with the exact one and also those obtained by earlier authors, and are found to be in very good agreement with each other. Further, it is shown that the numerical solutions satisfy the correct physical phenomena of the problem. (C) 2004 Elsevier Inc. All rights reserved.
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    A heat balance integral solution of the thermistor problem with a modified electrical conductivity
    (Elsevier Science Inc, 2006) Kutluay, S; Wood, AS; Esen, A
    A key driver of thermistor response is a thermally-dependent electrical conductivity. Several variants have been proposed in the literature and it is the purpose of this paper to explore the applicability of a bulk model by way of using the heat balance integral approach to predict the response of a positive temperature coefficient thermistor. Conclusions are presented regarding the sensitivity of the response to electrical conductivity. (c) 2005 Elsevier Inc. All rights reserved.
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    An isotherm migration formulation for one-phase Stefan problem with a time dependent Neumann condition
    (Elsevier Science Inc, 2004) Kutluay, S; Esen, A
    In this paper, we present a numerical scheme based on an isotherm migration formulation for one-dimensional, one-phase Stefan problem with a time dependent Neu-mann condition on the fixed boundary and a constant Dirichlet condition on the moving boundary. The numerical results obtained by the present method have been compared with exact one and also those obtained by earlier authors, and are found to be in very good agreement with each other. It is also shown that the numerical solution displays the expected convergence to the exact one as the mesh size is refined. (C) 2003 Elsevier Inc. All rights reserved.
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    A linearized numerical scheme for Burgers-like equations
    (Elsevier Science Inc, 2004) Kutluay, S; Esen, A
    A linearized implicit finite-difference method is presented to find numerical solutions of the one-dimensional Burgers-like equations. The method has been used successfully to obtain accurate numerical solutions even for small values of viscosity term v. Results obtained by the present method using a direct technique for some values of v have been compared with the exact values and are found to be in good agreement with each other. (C) 2003 Published by Elsevier Inc.
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    A lumped Galerkin method for solving the Burgers equation
    (Taylor & Francis Ltd, 2004) Kutluay, S; Esen, A
    A numerical solution of the one-dimensional Burgers equation is obtained using a lumped Galerkin method with quadratic B-spline finite elements. The scheme is implemented to solve a set of test problems with known exact solutions. Results are compared with published numerical and exact solutions. The proposed scheme performs well. A linear stability analysis shows the scheme to be unconditionally stable.
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    Numerical schemes for one-dimensional Stefan-like problems with a forcing term
    (Elsevier Science Inc, 2005) Kutluay, S
    Variable space grid and boundary immobilisation schemes based on the explicit finite difference method are applied to the one-phase Stefan-like problems with a forcing term in order to evaluate the temperature distribution and the interface movement (location and speed). The numerical results obtained by the two schemes have been compared with the exact values and are found to be in good agreement with each other. It is shown that the numerical solutions exhibit the expected convergence to the exact one as the mesh size is reduced. A von-Neumann stability analysis of each scheme is also investigated. (c) 2004 Elsevier Inc. All rights reserved.
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    Numerical solution of Burgers' equation by quadratic B-spline finite elements
    (Elsevier Science Inc, 2005) Özis, T; Esen, A; Kutluay, S
    In this paper, a Galerkin quadratic B-spline finite element method is used to solve numerically the one-dimensional Burgers' equation reduced by the Hopf-Cole transformation. The performance of the method is tested on two model problems involving moderately Reynolds numbers with known exact solutions. The obtained numerical results show that the method is efficient, robust and reliable for solving Burgers' equation accurately even involving high Reynolds numbers for which the exact solution fails. Computed results are compared with other numerical results in the literature. A stability analysis of the method is also investigated. (c) 2004 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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    The numerical solution of one-phase classical Stefan problem
    (Elsevier Science Bv, 1997) Kutluay, S; Bahadir, AR; Ozdes, A
    In 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.
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    A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method
    (Elsevier Science Inc, 2004) Esen, A; Kutluay, S
    In this paper, the enthalpy method based on suitable finite difference approximations has been applied to the one-dimensional moving boundary problem with a Neumann-type boundary condition known as the Stefan problem. The numerical results obtained by the hopscotch technique are compared with the exact solution of the problem. It is shown that all results are found to be in very good agreement with each other, and the numerical solution displays the expected convergence to the exact one as the mesh size is refined. (C) 2002 Elsevier Inc. All rights reserved.
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    Numerical solutions of the Burgers' equation by the least-squares quadratic B-spline finite element method
    (Elsevier Science Bv, 2004) Kutluay, S; Esen, A; Dag, I
    In this study, a least-squares quadratic B-spline finite element method for calculating the numerical solutions of the one-dimensional Burgers-like equations with appropriate boundary and initial conditions is presented. Three test problems have been studied to demonstrate the accuracy of the present method. Results obtained by the method have been compared with the exact solution of each problem and are found to be in good agreement with each other. A Fourier stability analysis of the method is also investigated. (C) 2003 Elsevier B.V. All rights reserved.
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    Numerical solutions of the thermistor problem by spline finite elements
    (Elsevier Science Inc, 2005) Kutluay, S; Esen, A
    This paper presents approximate steady-state solutions of a one-dimensional positive temperature coefficient (PTC) thermistor problem, having a step function electrical conductivity that is a highly non-linear function of the temperature, using subdomain collocation and Petrov-Galerkin methods based on spline finite elements. The resulting system of ordinary differential equations is solved by the usual Crank-Nicolson finite difference method using a variant of Thomas algorithm. It is shown that the numerical solutions obtained by the present methods exhibit the correct physical characteristics of the problem and, they are in very good agreement with the exact solution. A Fourier stability analysis of each method is also investigated. (C) 2004 Elsevier Inc. All rights reserved.
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    Numerical solutions of the thermistor problem with a ramp electrical conductivity
    (Elsevier Science Inc, 2004) Kutluay, S; Wood, AS
    This paper presents approximate steady-state solutions of a positive temperature coefficient thermistor problem, having a ramp electrical conductivity that is a highly non-linear function of the temperature, using a standard explicit finite difference method. It is shown that numerical solutions exhibit the correct physical characteristics of the problem and, they are in good agreement with the exact solution. (C) 2003 Elsevier Inc. All rights reserved.
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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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    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.