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Öğe An Approximate Solution of Burgers Equation by Differential Transform Method(2004) Ayaz, Fatma; Oturanç, GalipIn this paper, we investigate some applications of differential transform method for solving the linear and nonlinear partial differential equations with appropriate initial and boundary conditions. In order to test and comparison of the approximate solutions obtained from differential transform method where we have studied two test problems. In the first problem, a closed form solution of the heat equation, which can be obtained from Burgers' equation by omitting the nonlinear term in it, have been found easily. In the second problem, an approximate solution to the Burgers' equation under appropriate conditions has been found for only the small values of t (time variable) and viscosity, ν. For decreasing viscosity, which is difficult task in the solution, it has seen that no significant difference in the solution for 0<t<0.005. The results have showed that the method can easily be applied both linear and nonlinear partial differential equations.Öğe The differential transform methods for nonlinear function and its applications(Selcuk University Research Center of Applied Mathematics, 2008) Keskin, Yıldıray; Oturanç, GalipIn this study, new differential transform methods were presented to solve some nonlinear functional. The suggested methods are convenient for computational purpose because of its simple computer coding and its providing detailed solutions. The algorithms of the new methods were applied to the different types of nonlinear functional models.Öğe The Differential Transform Methods for Nonlinear Functions and Its Applications(2008) Keskin, Yıldıray; Oturanç, GalipIn this study, new differential transform methods were presented to solve some nonlinear functional. The suggested methods are convenient for computational purpose because of its simple computer coding and its providing detailed solutions. The algorithms of the new methods were applied to the different types of nonlinear functional models.Öğe Eigenvalue Analysis of Temperature Distribution in Composite Walls(John Wiley & Sons Ltd, 2001) Oturanç, Galip; Şahin, Ahmet Z.The transient heat conduction problem in two-layer composite wall is solved analytically using spectral analysis. Eigenvalues and corresponding eigenfunctions of the spectral problem for the temperature distribution in composite walls are analysed using the Rouche Theorem. The number of eigenvalues is obtained and the temperature distribution of this complicated problem is given by a formula with calculated eigenvalues. The analytical solution obtained is in explicit form and provides easy determination of temperature rise in heating and thawing applications of composite materials.Öğe The Lower Bounds for the Zeros of a Polynomial with Real or Complex Coefficients(1997) Taşçı, Dursun; Oturanç, GalipBu çalışmada matris normları ve Companion matrisi gözönüne alınarak reel ve kompleks katsayılı bir polinomun kökleri için bazı alt sınırlar elde edilmiştir.Öğe A new approach to the Thomas-Fermi equation(Selcuk University Research Center of Applied Mathematics, 2009) Oturanç, GalipIn this paper, a numerical method for solving Thomas -Fermi equation which plays very important role in applied mathematics and physics is proposed. The proposed scheme is based on the fractional differential transform method (FDTM) and Padapproximants. This method is approached to ?nd the numerical values of the initial slope of the Thomas-Fermi potential y'(0). In addition, the numerical results demonstrate the validity and applicability of the new technique. Finally, a comparison is made with existing results.Öğe A new approach to the Thomas-Fermi equation(2009) Oturanç, GalipIn this paper, a numerical method for solving Thomas -Fermi equa tion which plays very important role in applied mathematics and physics is proposed. The proposed scheme is based on the fractional differential transform method (FDTM) and Padé approximants. This method is approached to …nd the numerical values of the initial slope of the Thomas-Fermi potential y0(0). In addition, the numerical results demonstrate the validity and applicability of the new technique. Finally, a comparison is made with existing results.Öğe Performance Analysis of a Solar Cooker in Turkey(JOHN WILEY & SONS LTD, 2002) Oturanç, Galip; Özbalta, Necdet; Güngör, AliA box-type solar cooker is designed and its thermal performance is analysed experimentally. The cooker tracks the sun in two axes, altitude and sun azimuth, by hand control for hourly periods. The experimental results show that the tested cooker may be assumed suitable in some cooking processes for specific country conditions. Copyright (C) 2002 John Wiley Sons, Ltd.Öğe Reduced Differential Transform Method for Generalized KDV Equations(Mdpı, 2010) Keskin, Yıldıray; Oturanç, GalipIn this paper, a general framework of the reduced differential transform method is presented for solving the generalized Korteweg-de Vries equations. This technique doesn't require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. In addition, three test problems of mathematical physics are discussed to illustrate the effectiveness and the performance of the reduced differential transform method.Öğe Reduced Differential Transform Method for Solving Linear and Nonlinear Wave Equations(Springer International Publishing Ag, 2010) Keskin, Yıldıray; Oturanç, GalipReduced differential transform method (RDTM) is applied to various wave equations. To assess the accuracy of the solutions, we compare the results with the exact solutions and variational iteration method. The results reveal that the RDTM is very effective, convenient and quite accurate to systems of nonlinear equations.Öğe Setting up a high performance computing environment in the Ereğli Kemal Akman Vocational School(Selcuk University Research Center of Applied Mathematics, 2010) Kaçka, Serdar; Dündar, Özgür; Keskin, Yıldıray; Oturanç, GalipThe purpose of setting up this environment is to provide a tool for solving problems arising from engineering and science using parallel computing methods and achieving high performances in these solutions. In general, these kinds of problems require high processing powers. This environment is based on Beowulf Clusters which are widely used and cost-effective parallel computer architectures. A Beowulf Cluster is a parallel computer that is constructed of commodity hardware running commodity software. For this environment, eight computers with CeleronCPU's have been used. On each of these computers one of the popular distributions of Linux operating system, Fedora 11 has been installed. Then a local area network has been set up using a gigabit Ethernet switch. As the Message Passing Interface standard the high performance implementation of this standard, MPICH2 has been installed. This was the final step of installation. Finally, this environment has been tested with some parallel programs solving simple numerical analysis problems. The environment must be tested with more serious problems.Öğe Simple Correlations for Estimating the Energy Production of Turkey(Taylor & Francis Inc, 2002) Hepbaşlı, Arif; Oturanç, Galip; Kurnaz, Aydın; Ergin, Erkan; Genç, Aşır; İyit, NeslihanIndustrialization and population increases make the availability of potential energy in most areas a problem of great importance. Energy is considered to be a prime agent in the generation of wealth and also a significant factor in economic development. Most of the locations in Turkey have abundant energy resources, and energy utilization technologies can be profitably applied to these regions. In this study, we analyze the current status of Turkey's energy resources in terms of energy production and present simple correlations with high correlation coefficients for future projections. It is expected that this study will be helpful in dei,eloping highly applicable and productive planning for energy policies.Öğe Statistical Analysis of Solar Radiation Data(Taylor & Francis Inc, 2003) Oturanç, Galip; Hepbaşlı, Arif; Genç, AşırSolar radiation is the most important parameter in the design and study of solar energy conversion devices. In this study, statistical methods were used to analyze the solar radiation data for the city of Konya in the Mediterranean region of Turkey. Experimental data were obtained from the State Meteorological Station in Konya over a 9 year period from 1990 to 1998. The empirical coefficients a and b of the modified Angstrom-type regression equation were determined, while the values of the monthly average-daily clearness index (K-T) were calculated. A nonlinear model was also developed between the monthly average daily global radiation (H) and ambient temperature. The values of the monthly average-daily hours of bright sunshine (S) varied between 9.41 and 14.58. The values of K-T ranged from 0.54 to 0.60, averaged for the period studied. It may be concluded that the present model estimates the values of H for Konya reasonably well.Öğe Statistical Analysis of Solar Radiation Data Using Cubic Spline Functions(Taylor & Francis Inc, 2002) Genç, Aşır; Kınacı, İsmail; Oturanç, Galip; Kurnaz, Aydın; Bilir, Şefik; Özbalta, NecdetA cubic spline-type model has been developed to analyze the avarage daily total solar radiation data. This model has been found to perform significantly better than the other regression-type models. In this study, cubic spline functions have been used to analyze the solar radiation data of 5 years from 1994 to 1998 for Izmir. The reliability of the model has also been tested with a statistical hypothesis.
