Computational Mathmatics

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https://hdl.handle.net/20.500.11888/3205

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Numerical Methods for Solving Elliptic Boundary -Value Problems
(2005) Mithqal Ghalib Yousef Naji; Dr. Samir Matar
Elliptic Partial Differential Equations of second order have been studied using some numerical methods. This type of differential equations has specific applications in physical and engineering models. In most applications, first- order and second-order formulas are used for the derivatives. In this work higher order formulas such as: seven-points and nine-points formulas are used. Using these formulas will transform the partial differential equation into finite difference equations. To solve the resulting finite difference equations the following iterative methods have been used: Jacobi method, Gauss-Seidel method, Successive Over- Relaxation method (SOR) and Multigrain method. In this thesis, we found that multigrain methods are the most efficient among all other methods. The execution time for multigrain methods is of order three while the other methods is of order five.
Analysis of The Logistic Distribution Use in The Suppression Technique for Scalability in Multicast Routing
(2007) Hadi Ali Khalil Hamad; Dr. Mohammad Najib Ass'ad
The immense growth of the computer-supported communication systems, especially the internet, made it imperative to design protocols that have to be efficient and scalable to support the work of the networks infrastructure. By scalable is meant the ability of the protocol to cope with the requirements of groups of the communicating processes when they grow very large in size. The ever increasing demand on communication and the high capability of modern networks call continuously for efficient solutions to problems of communication. Among these solutions was the introduction of multicast routing and also the use of periodic unacknowledged messaging. Related to these two solutions of the problem of scalability, certain techniques were used to overcome this problem, including the suppression technique. This study deals with utilizing probabilistic distribution functions (pdfs) in the suppression technique with the aim of improvement of scalability of multicast routing in communication networks. The two most employed distributions in the suppression techniques are the uniform and the exponential distributions, the first outperforms the second in the performance time metric, while the exponential excels in the performance metric of extra messages. This study introduces a modified form of the logistic distribution as a candidate for use in the suppression technique and compares it with the two other above mentioned distributions. The MATLAB software was used in calculating the values of the performance metrics and in drawing the corresponding figures for comparing the results. The logistic distribution was proved to excel or compete with the other two pdfs in time performance metrics and to have a comparable performance in the overhead metrics.
Closeness Centrality and Epidemic Spreading in Networks
(2008) Fares Masuod Abdelgani Rabaya'; Dr . Sobhi Rosyea'; Dr . Adwan Yasin
This thesis is about the relation between the closeness centrality of the first infected node in the network and each of the total infection time that needs to infect all nodes in that network ,the infection rate for spreading epidemics in that network ,which measures the fraction of nodes those infected per unit time and the infection spreading power of that node ,that measures the power for each node to spread the epidemic to other uninfected nodes in that network. In this thesis, I deal with four types of networks ,unweight small and large networks and weighted small and large networks and study that relation in these four types. The importance of this work is when we find the closeness centrality and the infection spreading power of any node that help us understand which weakness or advantages this node has for maintenance or blocking dangers at the right time. In this work, I made some development in the SI model for the epidemic network in which most of authors consider the infection rate in that model assumed and constant. In this work I found that this infection rate is not constant but it depends on the closeness centrality of the first infected node in the network ,hence I suggest to replace the infection rate in the SI model by the closeness centrality of the first infected node in the network. The results obtained from this work show that each of the total infection time, the infection rate and the infection spreading power when any node infected first in the network depend on the closeness centrality for that node.
Cost Value Function Of Water Distribution Networks A Reliability-Based Approach Using Matlab
(2008) Khalid Ahmad “Mohammad” Hasan As-Sadiq; Dr. Mohammad Najeeb Ass'ad; Dr. Mohammad Nihad Almasri
Every community on Earth ought to find the appropriate means to distribute water from different sources to a consumption centers. In general, water distribution networks (WDN) attain this. Each network is composed of arches (to deliver water) and nodes (to consume the water delivered). The ability of any WDN to satisfy the requirements at each node under normal and abnormal conditions is one of the dimensions of its reliability. A method was introduced in this work to evaluate the reliability of a WDN for several combinations of diameters. A network solver was used to find the diameter combination successively. The results obtained from the network solver were saved in a text file. This file is then read by MATLAB, in order to do the necessary calculations. The system reliability for each diameter combination was computed. The values of the system reliability of each diameter combination are recorded as a vector in the MATLAB environment. The most important objective is the maximum of the system reliability of all these combinations, which has been achieved by MATLAB. For this maximum reliability value, we have determined the corresponding values of the cost, where each one represents a diameter combination. The minimum of these values is then determined using a computer code that was developed within the method. MATLAB was used to develop the computer program that converts the information into matrices, which make the required outcome easy to obtain and process. A hypothetical case study was developed to demonstrate methodology implementation. The results were composed of two important things: The computed reliability of any WDN and the way to find the least cost design with a value of reliability that is over a minimum boundary value. Another important thing is all the alternatives of reliability values that can be achieved with a specific budget that we already have.
Simulation in Queuing Models: Using Simulation at Beit-Eba Crossing Check-Point
(2008) Fatima Yousef Abdalla Barham; Dr. Mohammad Najeeb; Dr. Luai Malhis
This thesis consider some queuing models to determine the measures of performance of a model. The most important measures are the waiting time in the queue and the size of the queue. The queue we are studying is the Beit-eba crossing check-point for both people arriving and people departing from Nablus City. A comparison is made in order to determine the best fit model among two assumed models and the one under study(real one)using a suitable tool of simulation Sim Quick which performs process simulation within the Excel spreadsheet environment. To prove that we got good results for our study. We started by an assumed queue model and solve it analytically by the known formulas of queuing theory. Next, we use simulation by SimQuick to compare results, which showed a good agreement between analytical solution and simulation. The study showed that the single-channel queue is more efficient than the multiple-channels queues.
Error-Detecting and Error-Correcting Using Hamming and Cyclic Codes
(2009) Ne'am Hashem Ibraheem Ibraheem; Dr. "Mohammad Othman" Omran
In this thesis we provide an overview of two types of linear block codes: Hamming and cyclic codes. We study the generation, encoding and decoding of these codes as well as studying schemes and/or algorithms of error-detecting and error-correcting of these codes.
Data Compression with Wavelets
(2009) Rana Bassam Da'od Ismirate; Dr. Anwar Saleh
There are two types of data compression; the first is lossless(exact) and the second is lossy (approximate). In lossless compression, all details are reserved but high compression ratios can not be achieved and this type is not considered in this thesis. The other type is the loss compression where some details are lost in the process of compression. The size of the lost details is proportional with the the desired compression ratio which is controlled by the user. Using this type, high compression ratios can be achieved with acceptable resolution in the reconstructed data. In this thesis, a computational study of the classical Fourier transform and the relatively new wavelet transform is done. In addition, a computational comparison between the two major transforms shows that the wavelet transform is more efficient than the classical Fourier transform. The high compression ratios that can be achieved by wavelet transform lead to the introduction of several wavelet-based lossy data compression software. Examples of these are the image compressor JPEG2000 and the text compressor DJVU.
Bridging Centrality in Scale- Free Network Using Bridging Nodes as the Boundary of Clustering
(2009) Hind Ali Ahmed Eid; Dr. Sobhi Rozieh
Graph theory is one of the most popular fields in mathematics because if it's important applications in solving many problems in the real world and understanding many natural phenomena. This work focuses mainly on studying the scale-free networks and their properties. Moreover, it deals with the study of clustering methods and developing a new a new clustering algorithm by using the properties of scale-free networks. Bridging centrality of the graph together with Between ness centrality and bridging coefficients will also be investigated. Finally we will illustrate how bridging centrality is used in clustering. This will result in a new algorithm of clustering that is called Highest Bridging Centrality Cut algorithm (HCRC algorithm). We concluded that the HCRC algorithm depends on bridging centrality of the nodes.
Numerical Methods for Solving High-Order Boundary Value Problems
(2009) Basmah Othman Al Azzah; Dr.Sameer Matar
The Boundary Value-Problems (BVPs) either the linear or nonlinear problems have many life and scientific applications. Many studies concerned with solving second-order boundary-value problems using several numerical methods, and few studies concerned with especial cases of higher order boundary-value problems using several numerical methods to solve them. But However, in our thesis we concerned with the finite-difference methods for solving general high-order linear boundary-value problems (from order three up to order seven), modifying, and developing some finite-difference methods for solving especial eighth-order nonlinear boundary value problems to enable them solve any even-order problem beyond it. The main steps in this thesis depended on: -Using special finite-difference approximations for derivatives and formatting a formula that can be deal with endpoints that exceed the usual finite-difference formula for derivatives-Constructing linear system and solved it using the LU-decomposition method to decrease the computational processes. -Using The Richardson's Extrapolation method to get more accurate results. The numerical results for methods that appear in this thesis are good, but the errors in the methods increase when the order of the boundary-value problems becomes higher i.e. the fifth-order problem needs all derivatives , so by using approximations many times the errors will increase. Also the method accuracy depends on the boundary conditions values, that method has large error when are not given nor one of them, as well as the changes on the order of boundary conditions values. Besides that, this method requires long computing time and hard work while using very large equations that increase while the problem order increases.
Numerical Methods for Solving Differential Algebraic Equations
(2010) Samer Amin Kamel Abu Saa'; Dr.Sameer Matar
This study involves the implementation of two numerical methods for solving linear Deferential-algebraic equations (DAEs): Power series and Backward Difference Formula (BDF). It aims to facilitate dealing with DAEs by analyzing these two numerical methods, designing simple algorithms, and using MATLAB programs to code the two algorithms. Some numerical examples were implemented by the two methods, tables and figures were also presented in order to make comparisons and conclusions. This study concluded that Power Series is easier to use, time and effort saving. Furthermore, it is direct in tackling the problems. Finally, some difficult problems were solved by using this method. Other methods were unable to deal with.
Singular Two Points Boundary Value Problem
(2010) Sawsan Mohammed Anees Hamdan; Dr. Sameer Matar
A singular Two points boundary value problem occur frequently in mathematical modeling of many practical problems. To solve singular two points boundary value problem for certain ordinary differential equations having singular coefficients. Many numerical method such as shooting method, finite difference method and pade approximation methods, have been studied and analyzed.
An Inventory Control Model with (M/M/1) Queueing System and Lost Sales
(2011) Imad Ramzi Mohammed Jomah; Dr. Mohammed N. Asad
In this thesis We investigate M/M/1/ - queuing systems with inventory management, continuous review, and lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective system. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/ -system. We compute performance measures and derive optimality conditions under different order distributions. Although we can completely determine analytically the steady state probabilities for the system. We are able to derive functional relations for replenishment order size distributions that is in single server system with inventory. A computer programs were developed in this thesis to obtain the optimal policy.
Two-Sample Multivariate Test of Homogeneity Using Weighted Nearest Neighbours
(2012) Areej Ali Said Barakat; Dr. Mohammad Najib Ass'ad
In this research we proposed a two-sample test related to that proposed by Schilling and Barakat tests , by taking into account all the points and their positions according to the nearest to the nearest technique starting from the point which represents the median . Schilling did not do that ,since he just applied his test by using the first nearest neighbour , two nearest neighbours, or first three nearest neighbours and we also took the nearest to the nearest point to the median which Barakat did not do since he took all the nearest neighbours to the starting point. That’s to say in our proposed test we will give more weight to the most nearest neighbour to the starting point which is the median than the remaining nearest neighbours and so on. We proposed a test statistic and proved that its distribution is normal. We construct a MATLAB computer program to compute our test statistic.
Analytical and Numerical Treatment of Maxwell's Equations
(2012) Mai "Muhammad Ribhe" Asad Musmar; Prof. Naji Qatanani
Maxwell's equations are one of the most important models in different fields. It describes electromagnetic phenomena such as micro, radios and radar waves. The modeling of systems involving electromagnetic waves is widely spread and has attracted the attention of many authors and researchers. In this work, we will present some important analytical and numerical aspects of Maxwell's equations. We will review some basic properties of electromagnetic theory, namely: electromagnetic fields, magneto-static fields, and time varying fields. Moreover, we will use these physical properties to derive Maxwell's equations in various forms. Though, it is well known that Maxwell's equations are hard to solve analytically, however, we will attempt to use some well known analytical methods to solve these equations in some particular domains such as a sphere and a circular cylinder. Such analytical methods include: separation of variables, series expansion method, conformal mapping and integral methods such as Laplace transforms and cosine and sine Fourier transforms. Numerical methods for solving Maxwell's equations are extensively used nowadays and are usually referred to as Computational Electro-magnetic (CEM). Here the Finite Difference and Finite Difference Time Domain Method (FDTDM) known for its simplicity and efficiency will be proposed to solve Maxwell's equations. And the Yee Algorithm will also be illustrated. Moreover, the convergence, stability and error analysis for these numerical methods will also be investigated.
Analytical and Numerical Solutions of Magnetohydrodynamic Flow Problems
(2013) Abdel Latif Khaleel Sa’ad Aldin; rof. Naji Qatanani
The MagnetoHydreoDynamic flow ( MHD ) is one of the most important topics in mathematical physics due to its wide range of applications . In this work we present some analytical and numerical solutions for some MHD problems . The MHD flow past an impulsively started infinite horizontal plate in a rotating system and unsteady MHD flow through two parallel porous flat plates are considered. In this work an exact analytical solution for these problems based on Laplace transform method has been constructed and analyzed. This involves transforming the coupled partial differential equations into a single equation. For the numerical treatment of these problems we use the finite difference scheme and then implementing a computer software “ MAPLE 15“ to obtain some numerical results.
Numerical Treatment of The Fredholm Integral Equations of the Second Kind
(2013) Nujood Asad Abdulrahman Rihan; Prof. Naji Qatanani
In this thesis we focus on the mathematical and numerical aspects of the Fredholm integral equation of the second kinddue to their wide range of physical application such as heat conducting radiation, elasticity, potential theory and electrostatics. After the classification of these integral equations we will investigate some analytical and numerical methods for solving the Fredholm integral equation of the second kind. Such analytical methods include: the degenerate kernel methods, converting Fredholm integral equation to ODE, the Adomain decomposition method, the modified decomposition method andthe method of successive approximations. The numerical methods that will be presented here are: Projection methods including collocation method and Galerkin method, Degenerate kernel approximation methods and Nyström methods. The mathematical framework of these numerical methods together with their convergence properties will be analyzed. Some numerical examples implementing these numerical methods have been obtained for solving a Fredholm integral equation of the second kind. The numerical results show a closed agreement with the exact solution.
Error Analysis and Stability of Numerical Schemes for Initial Value problems “IVP’s”
(2013) Imad Omar Faris Kayid; أ.د. ناجي قطناني
Most of initial value problems are natural phenomena written in the language of mathematics. Solving these initial value problems is one of the most challenging fields in mathematics, because of the mathematicians’ continuous desire of exactness. This work focuses mainly on developing algorithms and programs to construct higher order Taylor’s methods for approximating the solution of first order initial value problems, systems of first order initial value problems and higher order initial value problems. Moreover, it concentrates on studying error and stability of numerical methods for solving initial value problems. For this purpose, we developed programs to find the error amplification functions of Taylor’s and Runge-Kutta methods and to plot boundaries of stability regions for these methods and other methods. We concluded that with the programs we developed, higher order Taylor’s methods could be a good choice for approximating solutions of a wide range of initial value problems.
Analytical and Numerical Solutions of Volterra Integral Equation of the Second Kind
(2014) Feda’ Abdel Aziz Mustafa Salameh; Prof. Naji Qatanani
In this thesis we focus on the analytical and numerical aspects of the Volterra integral equation of the second kind. This equation has wide range of applications in physics and engineering such as potential theory, Dirichlet problems, electrostatics, the particle transport problems of astrophysics, reactor theory, contact problems, diffusion problems and heat transfer problems. After introducing the types of integral equations, we will investigate some analytical and numerical methods for solving the Volterra integral equation of the second kind. These analytical methods include: the Adomian decomposition method, the modified decomposition method, the method of successive approximations, the series solution method and the conversion to initial value problem. For the numerical treatment of the Volterra integral equation we will implement the following numerical methods: Quadrature methods (Trapezoidal rule, Runge-Kutta method of order two, the fourth order Runge-Kutta method), Projection methods including collocation method and Galerkin method and the Block method. The mathematical framework of these numerical methods together with their convergence properties will be presented. These numerical methods will be illustrated by some numerical examples. Comparisons between these methods will be drawn. Numerical results show that the Trapezoidal rule has proved to be the most efficient method in comparison to the other numerical methods.
Wavelets Numerical Methods for Solving Differential Equations
(2015) Yousef Mustafa Yousef Ahmed Bsharat; Dr. Anwar Saleh
In this thesis, a computational study of the relatively new numerical methods of Haar wavelets for solving linear differential equations is used. A comparison between the new method and some classical methods for linear differential equations has been made. The aim is to show the efficiency of the presented method and its advantage over other method. The new method is simple and its numerical results are close or more accurate than some classical methods
Confidence – based Optimization for the Single Period Inventory Control Model
(2016) Thana’a Hussam eddin Amin Abu Sa’a; Dr.Mohammad Ass’ad
In this thesis we introduce the issue of demand estimation. We study a problem of controlling the inventory of a single item over a single period with stochastic demand in which the distribution of the demand has an unknown parameter. We assume that the decision maker has a past demand sample and the demand distribution is known but some of its parameters are not known. We introduce some approaches to estimate the unknown parameter and depending on results from estimating the unknown parameter we identify a range of order quantities that-with confidence coefficient – contains the optimal order quantity, and then we construct an interval for the estimated expected cost that the manager will pay if he orders any quantity from the range of candidate quantities. We consider three cases, the demand has a Binomial distribution with unknown parameter , and the demand has a Poisson distribution with unknown parameter , also we consider the case in which the demand has an Exponential distribution with unknown parameter . We present numerical examples in order to clarify our strategy and to show how the confidence interval approach complements with the point estimation approach in order to give the best outlook to the manager to take a decision that achieve an optimal profit.

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