In this thesis, the two-dimensional, unsteady, laminar and incompressible fluid flow problems governed by partial differential equations are solved by using dual reciprocity boundary element method (DRBEM). First, the governing equations are transformed to the inhomogeneous modified Helmholtz equations, and then the fundamental solution of modified Helmholtz equation is used for obtaining boundary element method (BEM) formulation. Thus, all the terms in the equation except the modified Helmholtz operator are considered as inhomogeneity. All the inhomogeneity terms are approximated by using suitable radial basis functions, and corresponding particular solutions are derived by using the annihilator method. Transforming time dependent partial differential equations to the form of inhomogeneous modified Helmholtz equations in DRBEM application enables us to use more information from the original governing equation. These are the main original parts of the thesis. In order to obtain modified Helmholtz equation for the time dependent partial differential equations, the time derivatives are approximated at two time levels by using forward finite difference method. This also eliminates the need of another time integration scheme, and diminishes stability problems. Stream function-vorticity formulations are adopted in physical fluid dynamics problems in DRBEM by using constant elements. First, the procedure is applied to the lid-driven cavity flow and results are obtained for Reynolds number values up to 2000. The natural convection flow is solved for Rayleigh numbers between 10^3 to 10^6 when the energy equation is added to the Navier-Stokes equations. Then, double diffusive mixed convection flow problem defined in three different physical domains is solved by using the same procedure. Results are obtained for various values of Richardson and Reynolds numbers, and buoyancy ratios. Behind these, DRBEM is used for the solution of natural convection flow under a magnetic field by using two different radial basis functions for both vorticity transport and energy equations. The same problem is also solved with differential quadrature method using the form of Poisson type stream function and modified Helmholtz type vorticity and energy equations. DRBEM and DQM results are obtained for the values of Rayleigh and Hartmann numbers up to 10^6 and 300, respectively, and are compared in terms of accuracy and computational cost. Finally, DRBEM is used for the solution of inverse natural convection flow under a magnetic field using the results of direct problem for the missing boundary conditions.

This thesis presents the Differential Quadrature Method (DQM) for solving time-dependent or heat conduction problem. DQM discretizes the space derivatives giving a system of ordinary differential equations with respect to time and the fourth order Runge Kutta Method (RKM) is employed for solving this system. Stabilities of the ordinary differential equations system and RKM are considered and step sizes are arranged accordingly. The procedure is applied to several time dependent diffusion problems and the solutions are presented in terms of graphics comparing with the exact solutions. This method exhibits high accuracy and efficiency comparing to the other numerical methods.

In this thesis, a mixed integer linear program is used to formulate the optimization process of a wind farm. As a start point, a grid was superimposed into the wind farm, in which grid points represent possible wind turbine locations. During the optimization process, proximity and wind interference between wind turbines were considered in order to found the power loss of the wind farm. Power loss was analyzed by using wind interference coefficient, which is a function of wind intensity interference factor (WIIF), weibull distribution and power of the wind turbines. Two different programs / Genetic Algorithm and Lingo, were used to solve the MILP optimization formula and results were compared for different cases in the conclusion part.

Threshold dynamics used to control the spread of the disease in infectious disease phenomena has an overwhelming importance and interest in mathematical epidemiology. One of the famous threshold quantity is known to be the basic reproduction ratio. Its formulation as well as computation is the main concern of infectious diseases. The aim of this thesis is to analyze the basic reproduction ratio in both autonomous and periodic systems via defining R0 as the spectral radius of the next generation operator. This thesis presents the vector host model for the diseases Dengue fever and avian influenza. As emerging of the diseases shows periodicity, systems of periodic ordinary differential equations are considered for both types of diseases. Simple implementation of the time-averaged systems gives rise to the comparison of these with the periodic systems. Thus, we investigate the occurence of the existence of underestimation or overestimation of the basic reproduction ratio in timeaveraged systems.

This study investigates the accuracy and efficiency of several flux splitting methods for the compressible, two-dimensional Euler equations. Steger-Warming flux vector splitting method, Van Leer flux vector splitting method, The Advection Upstream Splitting Method (AUSM), Artificially Upstream Flux Vector Splitting Scheme (AUFS) and Roe&rsquo / s flux difference splitting schemes were implemented using the first- and second-order reconstruction methods. Limiter functions were embedded to the second-order reconstruction methods. The flux splitting methods are applied to subsonic, transonic and supersonic flows over NACA0012 airfoil, as well as subsonic, transonic and supersonic flows in a channel. The comparison of the obtained results with each other and the ones in the literature is presented. The advantages and disadvantages of each scheme among others are identified.

A spectral element solver program using MATLAB is written for the solution of Poisson and Helmholtz equations. The accuracy of spectral methods (p-type high order) and the geometric flexibility of the low-order h-type finite elements are combined in spectral element methods. Rectangular elements are used to solve Poisson and Helmholtz equations with Dirichlet and Neumann boundary conditions which are homogeneous or non homogeneous. Robin (mixed) boundary conditions are also implemented. Poisson equation is also solved by discretising the domain with curvilinear quadrilateral elements so that the accuracy of both isoparametric quadrilateral and rectangular element stiffness matrices and element mass matrices are tested. Quadrilateral elements are used to obtain the stream functions of the inviscid flow around a cylinder problem. Nonhomogeneous Neumann boundary conditions are imposed to the quadrilateral element stiffness matrix to solve the velocity potentials.

This thesis uses Spline-based model, which was developed by McCulloch, and parsimonious model, which was developed by Nelson-Siegel, to estimate the yield curves of zero-coupon bonds in Turkey. In this thesis, we construct the data by using Turkish secondary government zero-coupon bond data, which contain the data from January 2005 to June 2005. After that, relative performances of models are compared using in-sample goodness of fit. As a result, we see that performance of McCulloch model in fitting yield is better than that of Nelson-Siegel model.

Many interacting complex systems in biology, in physics, in technology and social systems, can be represented in a form of large networks. These large networks are mathematically represented by graphs. A graph is represented usually by the adjacency or the Laplacian matrix. Important features of the underlying structure and dynamics of them can be extracted from the analysis of the spectrum of the graphs. Spectral analysis of the so called normalized Laplacian of large networks became popular in the recent years. The Laplacian matrices of the empirical networks are in form of unstructured large sparse matrices. The aim of this thesis is the comparison of different eigenvalue solvers for large sparse symmetric matrices which arise from the graph theoretical epresentation of undirected networks. The spectrum of the normalized Laplacian is in the interval [0 2] and the multiplicity of the eigenvalue 1 plays a particularly important role for the network analysis. Moreover, the spectral analysis of protein-protein interaction networks has revealed that these networks have a different distribution type than other model networks such as scale free networks. In this respect, the eigenvalue solvers implementing the well-known implicitly restarted Arnoldi method, Lanczos method, Krylov-Schur and Jacobi Davidson methods are investigated. They exist as MATLAB routines and are included in some freely available packages. The performances of different eigenvalue solvers PEIG, AHBEIGS, IRBLEIGS, EIGIFP, LANEIG, JDQR, JDCG in MATLAB and the library SLEPc in C++ were tested for matrices of size between 100-13000 and are compared in terms of accuracy and computing time. The accuracy of the eigenvalue solvers are validated for the Paley graphs with known eigenvalues and are compared for large empirical networks using the residual plots and spectral density plots are computed.

In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M. For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.

In this study, the settlement behavior of the piled raft foundations resting on overconsolidated clays under uniform loading, is investigated for different pile configurations and load levels. A total of 100 plane &ndash / strain and three &ndash / dimensional finite element analyses are carried out and the results of these analyses are compared both with each other and with the results presented by Reul &amp / Randolph (2004). The material parameters used in the analysis are selected mainly referring to the previous studies cited above on the same subject and slight modifications are made for convenience in the analysis. The analysis method and the applied pile configurations and load levels are directly taken from the reference study, excluding the soil model employed. A drained Mohr &ndash / Coulomb failure criteria is employed in the analysis of this study in modeling the soil instead of an elastoplastic model which was used in the analysis of the reference study. The results are evaluated for the average and differential settlements of the foundations and it is seen that / although the average and differential settlements calculated in this study are not always very close to the values calculated in the reference study, the calculated settlement reduction factors due to piles (especially for the average settlements) compared well with the findings of the reference study for all pile configurations and load levels considered. Based on this, a new approach is suggested to estimate the average settlements of the piled raft foundations. Moreover, correction factors are recommended in order to estimate the average settlements of the piled rafts by directly using the programs employed throughout the thesis.