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    A novel hybrid method for better evaluation: Evaluating university instructors teaching performance by combining conventional content analysis with fuzzy rule based systems
    (PERGAMON-ELSEVIER SCIENCE LTD, 2011) Basaran, Murat Alper; Kalayci, Nurdan; Atay, Mehmet Tarik
    Even though engineering and applied sciences deal with numerical data, they have successfully implemented fuzzy logic by using fuzzy rule based (FRB) systems by verbalizing data. On the other hand, social sciences such as sociology, education and physiology transform verbal type data into numerical values by using Likert type scale. Despite the fact that fuzzy set theory deals with verbal data very powerfully, social science fields in general have avoided to implement it to their verbal data up until now. One of the most active research areas in education field which generates verbal data is student evaluation of teaching (SET) questionnaires which are related to Total Quality Management applications in most of the competitive universities in the world. In this paper, we propose a novel hybrid method, which combines conventional content analysis (CCA) method and FRB systems and this new hybrid method is more suitable for the verbal data obtained from SET questionnaires. This novel CCA-FRB (conventional content analysis based fuzzy rule based systems) method uses a sample of 138 junior students from Gazi University in Turkey to implement the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.
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    Analysis of convective straight and radial fins with temperature-dependent thermal conductivity using variational iteration method with comparison with respect to finite element analysis
    (HINDAWI LTD, 2007) Coskun, Safa Bozkurt; Atay, Mehmet Tarik
    In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems. Copyright (C) 2007.
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    Comment to paper entitled "Application of the analytical hierarchy process in the selection of desalination plants" in 174 (2005) 97-108
    (ELSEVIER SCIENCE BV, 2010) Basaran, Murat Alper; Dilek, Emine Figen; Atay, Mehmet Tarik
    The paper entitled "Application of the analytical hierarchy process in the selection of desalination plants" used Analytical Hierarchy Process in order to choose the best desalination plant using four alternatives (technologies) and seven selection criteria. In the conclusion part of the above mentioned study, the final decision made by the authors was that the RO process was the most appropriate technology and the most important criteria was the cost. However, this suggestion cannot be inferred from the results given by the authors since some matrices are inconsistent matrices which means that revising and re-scaling those matrices must be necessary before continuing further calculations, and there are also many minor and major miscalculations that exist throughout the paper. (C) 2010 Elsevier B.V. All rights reserved.
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    Comparative Analysis of Power-Law Fin-Type Problems Using Variational Iteration Method and Finite Element Method
    (HINDAWI PUBLISHING CORPORATION, 2008) Atay, Mehmet Tarik; Coskun, Safa Bozkurt
    Variational iteration method is applied to examine the temperature distribution within a single fin with a one-dimensional steady-state nonlinear heat conduction equation. Variation of temperature due to different levels of nonlinearities is analyzed. The results obtained by means of variational iteration method are compared with the results obtained from finite element method. A fourth iteration variational iteration solution is used in all cases considered. An error analysis is also conducted to evaluate the performance of proposed solution technique. The results have shown that variational iteration method is a powerful solution technique in the analysis of power-law fin-type problems. Copyright (C) 2008 M. T. Atay and S. B. Coskun.
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    Computation of Eigenvalues of Sturm-Liouville Problems using Homotopy Perturbation Method
    (FREUND PUBLISHING HOUSE LTD, 2010) Atay, Mehmet Tarik; Kartal, Senol
    In this paper, a recently proposed analytical approximation technique, namely Homotopy Perturbation Method (HPM) is presented to compute eigenvalues of second and fourth order Sturm-Liouville problems. These types of equations appear in engineering applications such as vibration, elastic stability problems, which are great importance in engineering practice and real world applications. The presented technique is formulated and then applied to number of Sturm-Liouville problem cases for which solutions were obtained numerically. An easy to use feature of the method is promising for applying to such boundary value problems.
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    Determination of Buckling Loads and Mode Shapes of a Heavy Vertical Column under its Own Weight Using the Variational Iteration Method
    (WALTER DE GRUYTER GMBH, 2010) Okay, Fuad; Atay, Mehmet Tarik; Coskun, Safa Bozkurt
    This paper applies the variational iteration method for finding buckling loads and mode shapes of a heavy column. The study shows efficiency of the method and accuracy of the obtained analytic approximate solution.
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    Determination of Buckling Loads of Tilted Buckled Column with Varying Flexural Rigidity Using Variational Iteration Method
    (FREUND PUBLISHING HOUSE LTD, 2010) Atay, Mehmet Tarik
    In this paper, Variational Iteration Method (VIM) is applied for finding buckling loads of a tilted buckled column with varying flexural rigidity, which is an important engineering problem in structural analysis and design considerations. In the cases where determination of exact solutions of tilt-buckling problems may not be possible, usage of this new technique will give researchers a powerful tool for determining them. This study shows the efficiency of the method and accuracy of the resulting analytic approximate solution for the problem.
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    Determination of buckling loads of tilted buckled column with varying flexural rigidity using variational iteration method
    (2010) Atay, Mehmet Tarik
    In this paper, Variational Iteration Method (VIM) is applied for finding buckling loads of a tilted buckled column with varying flexural rigidity, which is an important engineering problem in structural analysis and design considerations. In the cases where determination of exact solutions of tilt-buckling problems may not be possible, usage of this new technique will give researchers a powerful tool for determining them. This study shows the efficiency of the method and accuracy of the resulting analytic approximate solution for the problem. ©Freund Publishing House Ltd.
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    Determination of critical buckling load for elastic columns of constant and variable cross-sections using variational iteration method
    (PERGAMON-ELSEVIER SCIENCE LTD, 2009) Coskun, Safa Bozkurt; Atay, Mehmet Tarik
    In this paper, variational iteration method (VIM) is applied to the problem of determination of critical buckling loads for Euler columns with constant and variable cross-sections. VIM is a powerful method for the solution of nonlinear ordinary and partial differential equations and integral equations. Hence it is a suitable approach for the analysis of engineering problems where an exact solution is difficult to obtain. This study presents the application of VIM to various buckling cases and results are produced for columns with different support conditions and with different variation of cross-sections. The results obtained are accurate which show that variational iteration method is a very efficient technique in the analysis of elastic stability problems. (C) 2009 Elsevier Ltd. All rights reserved.
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    Determination of Critical Buckling Loads for Variable Stiffness Euler Columns Using Homotopy Perturbation Method
    (WALTER DE GRUYTER GMBH, 2009) Atay, Mehmet Tarik
    In this paper, a new perturbation method namely, Homotopy Perturbation Method (HPM), is applied to buckling of non-uniform columns problem, which is an important engineering problem, because of the fact that determining the buckling loads are important steps in structural analysis and design applications. Columns are primary structural forms and there are numerous studies related to this subject. Application of this new method (HPM) will give researchers a new and powerful tool for solving buckling problems for which finding an exact analytical solution may not be possible. An important point of this technique is, in contrast to traditional perturbation methods, that this new technique does not require a small parameter in an equation to be solved. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p is an element of [0,1] is constructed and imbedding parameter is considered as an expanding parameter. The paper shows the efficiency of the method and accuracy of the obtained analytic approximate solution for the problem.
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    Effects of nonlinearity on the variational iteration solutions of nonlinear two-point boundary value problems with comparison with respect to finite element analysis
    (HINDAWI LTD, 2008) Atay, Mehmet Tarik; Coskun, Safa Bozkurt
    Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions. Copyright (C) 2008 M. T. Atay and S. B. Coskun.
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    Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method
    (PERGAMON-ELSEVIER SCIENCE LTD, 2009) Atay, Mehmet Tarik; Coskun, Safa Bozkurt
    In this paper, analysis of elastic stability for continuously restrained Euler columns is conducted by means of variational iteration method (VIM). A uniform homogeneous column is assumed to be restrained along its length. The restraint considered in this study is an elastic foundation model in engineering practice and it is of great interest to foundation engineers. Hence, the variation of the critical buckling loads with the stiffness of elastic restraint is investigated using VIM for the restrained columns with different end conditions. Obtaining analytical solutions for these types of problems is not a simple procedure since the equations of stability criteria are highly nonlinear. This study presents the application of VIM for obtaining exact solutions for continuously restrained Euler columns. The study proves that VIM is a very efficient and promising approach in the elastic stability analysis of specified problems. (C) 2009 Elsevier Ltd. All rights reserved.
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    Fin efficiency analysis of convective straight fins with temperature dependent thermal conductivity using variational iteration method
    (PERGAMON-ELSEVIER SCIENCE LTD, 2008) Coskun, Safa Bozkurt; Atay, Mehmet Tarik
    For enhancing heat transfer between primary surface and the environment, utilization of radiating extended surfaces are common. Especially for large temperature differences; variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze the efficiency of convective straight fins with temperature dependent thermal conductivity. VIM produces analytical expressions for the solution of nonlinear differential equations. In order to show the effectiveness of Variational iteration method (VIM). the results obtained from VIM analysis is compared with available solutions obtained using Adomian decomposition method (ADM) and the results from finite element analysis. This work assures that VIM is it promising method for the efficiency analysis of convective straight fin problems. (C) 2008 Elsevier Ltd. All results reserved
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    Homotopy perturbation method for free vibration analysis of beams on elastic foundation
    (IOP PUBLISHING LTD, 2010) Ozturk, Baki; Coskun, Safa Bozkurt; Koc, Mehmet Zahid; Atay, Mehmet Tarik; Khalili, N; Valliappan, S; Li, Q; Russell, A
    In this study, the homotopy perturbation method (HPM) is applied for free vibration analysis of beam on elastic foundation. This numerical method is applied on a previously available case study. Analytical solutions and frequency factors are evaluated for different ratios of axial load N acting on the beam to Euler buckling load, N-r. The application of HPM for the particular problem in this study gives results which are in excellent agreement with both analytical solutions and the variational iteration method (VIM) solutions for the case considered in this study and the differential transform method (DTM) results available in the literature.
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    Magnus Expansion Method for Solving Singularly Perturbed Turning Point Problems Having Boundary Layers
    (AMER INST PHYSICS, 2015) Kome, Sure; Atay, Mehmet Tarik; Eryilmaz, Aytekin; Kome, Cahit; Simos, TE; Tsitouras, C
    In this paper, Magnus expansion method which is based on Lie groups and Lie algebras is presented to solve singularly perturbed boundary value problems having boundary layers. Numerical results are obtained by using different step sizes and small epsilon values which makes the problem stiff or nonstiff. In addition, maximum errors norms with L-infinity are tabulated in detail to show efficiency of the method.
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    Numerical and Soft Computing Methods for Characteristic Value Problems of ODE and ODEs Systems
    (HINDAWI PUBLISHING CORPORATION, 2013) Atay, Mehmet Tarik; Simonetti, Biagio; Coskun, Safa Bozkurt; Venkatesan, D.; Basaran, Murat Alper; Squillante, Massimo
    [Abstract Not Available]
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    Numerical Solutions of Linear and Nonlinear Lane-Emden Type Equations Magnus Expansion Method
    (AMER INST PHYSICS, 2015) Kome, Cahit; Atay, Mehmet Tarik; Eryilmaz, Aytekin; Kome, Sure; Simos, TE; Tsitouras, C
    In this paper, we study on the numerical solutions of linear and nonlinear singular initial value problems of Lane-Emden type with different orders of Magnus expansion method (MEM). The proposed method is different from other numerical techniques as it is based on lie groups and lie algebras. To show the efficiency of the method, we present approximate and exact values and also L-infinity error norms with detailed tables and figures.
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    The Semianalytical Solutions for Stiff Systems of Ordinary Differential Equations by Using Variational Iteration Method and Modified Variational Iteration Method with Comparison to Exact Solutions
    (HINDAWI LTD, 2013) Atay, Mehmet Tarik; Kilic, Okan
    The Variational Iteration Method (VIM) and Modified Variational Iteration Method (MVIM) are used to find solutions of systems of stiff ordinary differential equations for both linear and nonlinear problems. Some examples are given to illustrate the accuracy and effectiveness of these methods. We compare our results with exact results. In some studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method. Comparisons with exact solutions reveal that the Variational Iteration Method (VIM) and the Modified Variational Iteration Method (MVIM) are easier to implement. In fact, these methods are promising methods for various systems of linear and nonlinear stiff ordinary differential equations. Furthermore, VIM, or in some cases MVIM, is giving exact solutions in linear cases and very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.