Galip Oturanç

Reduced Differential Transform Method for Partial Differential Equations

Recently differential transform method (DTM) has been used to solve various partial differential equations. In this paper, an alternative approach called the reduced differential transform method (RDTM) is presented to overcome the demerit of complex calculation of differential transform method. 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.

n-Dimensional differential transformation method for solving PDEs

This paper presents the generalization of the differential transformation method to n-dimensional case in order to solve partial differential equations (PDEs). A distinctive practical feature of this method is its ability to solve especially nonlinear differential equations efficiently. We apply our results to a few initial boundary-value problems to illustrate the proposed method.

Estimation of Wind Power Potential Using Weibull Distribution

The main objective of the present study is to estimate wind power potential using the two Weibull parameters of the wind speed distribution function, the shape parameter k (dimensionless) and the scale parameter c (m/s). In this regard, a methodology that uses three various techniques (maximum likelihood, least squares, and method of moments) for estimating the Weibull parameters was given first. The methodology was then applied to a region in Turkey. Finally, the parameter techniques were compared to Monte-Carlo simulation in different sample sizes, and the best parameter estimation techniques belonging to the sample sizes were also determined.

Approximate Solutions of Generalized Pantograph Equations by the Differential Transform Method

Delay differential equations (DDEs) are a large and important class of dynamical systems. Many phenomena in applied sciences can be successfully modelled by these equations [1-4]. For example, in natural or control systems, a controller monitors the state of the system and make adjustments to the system based on its observations. Therefore a delay occurs between the observation and the control action. In particular, they become powerful models in explaining physical phenomena when ODEbased models fail. There are different kinds of DDEs studied by various methods [5-12] In this paper, we deal with the generalization of the pantograph equation which is studied in [5,6] given by

The differential transform approximation for the system of ordinary differential equations

We present a comparative study of the differential transformation for solving systems of linear or non-linear ordinary differential equations (ODEs). A remarkable practical feature of this method is its ability to solve the system of linear or non-linear differential equations efficiently. This method also enables us to control the truncation error by adjusting the step size used in the numerical scheme. We apply our results to some initial value problems to demonstrate the ability of the method to solve systems of differential equations.

A new analytical approximate method for the solution of fractional differential equations

A new analytical approximate method for the solution of fractional differential equations is presented. This method, which does not require any symbolic computation, is important as a tool for scientists and engineers because it provides an iterative procedure for obtaining the solution of both linear and non-linear fractional differential equations. The effectiveness of the proposed method is illustrated with some examples.

Assessment of wind characteristics for energy generation

Wind technology in Turkey has gained considerable maturity over the last five years, and wind energy projects are becoming commercially attractive in the country. In practice, it is essential to describe the variation of wind speeds for optimizing the design of the systems resulting in less energy generating costs. The wind variation for a typical site is usually described using the so-called Weibull distribution. In this study, the two Weibull parameters of the wind speed distribution function, the shape parameter k (dimensionless) and the scale parameter c (m/s), were computed from the wind speed data for Aksehir in Konya, located in Central Anatolia in Turkey (latitude: 38.35° and longitude: 31.42°). Wind data, consisting of hourly wind speed records over a 6 year period, 1997–2002, were obtained from the Aksehir State Meteorological Station. Based on the experimental data, it was found that the numerical values of both Weibull parameters (k and c) for Aksehir vary over a wide range. The yearly values of k range from 1.756 to 2.076, while those of c are in the range of 2.956 to 3.444. Average seasonal Weibull distributions for Aksehir are given. The wind speed distributions are represented by Weibull distribution and also by Rayleigh distribution with a special case of the Weibull distribution for k = 2. The Rayleigh distribution is found to be suitable to represent the actual probability of wind speed data for the site studied.

Simple Correlations for Estimating the Energy Production of Turkey

Industrialization 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 Turkeys energy resources in terms of energy production and present simple corrections with high correlation coefficients for future projections. It is expected that this study will he helpful in developing highly applicable and productive planning for energy policies.

Statistical Analysis of Solar Radiation Data

Solar 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 Angström-type regression equation were determined, while the values of the monthly average-daily clearness index (KT ) 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 KT 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.

Statistical Analysis of Solar Radiation Data Using Cubic Spline Functions

A 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 G zmir. The reliability of the model has also been tested with a statistical hypothesis.