ABSTRACT This study is about Overview solutions of nonlinear differential equations and its applications. It consists of four chapters where by the first chapter is devoted on the general overview solutions of differential equations. The second chapter deals with numerical solutions of differential equations. It provides the numerical values of the differential equations with initial conditions or boundary conditions within the given range or interval. The third chapter is about the fixed po...

ABSTRACT This dissertation contains materials on numerical solutions based on elliptic differential equations only appropriate for senior level undergraduate or beginning level graduate students. The reader based on this dissertation should have had introductory courses in Calculus, linear algebra and general numerical analysis. A formal course in ordinary or partial differential equations would be useful. In our study, it should be understood that, there are many procedures that come under ...

Abstract The aim of this study was to assess the impact on teaching and learning using the LSTT (Language Supportive Teaching and Textbooks) project’s bilingual Mathematics textbook chapters among Form One students in selected rural community secondary schools in Tanzania. LSTT project was introduced in Tanzania in 2013 to enhance language supportive teaching among the disadvantaged rural groups identified as less competent in foreign languages. The study employed both quantitative and qua...

ABSTRACT Several methods which have been adopted to analyze multi-category data yields unsatisfactory results because of strict assumptions regarding normality, linearity, and homoscedasticity. As a result, Multinomial logistic regression is considered as an alternative because it does not assume normality, linearity, or homoscedasticity (Hosmer & Lemeshow, (2000)). The study attempted to use Maximum likelihood estimation and predicted probability to model Maternal Health Care Services data b...

Table of Contents List of Tables List of Figures Acknowledgement Chapter One Introduction Background Information Statement of Problems Purpose and Objective of Study Outline Chapter Two - Estimators in Adaptive Cluster Sampling Introduction Ordinary Estimators in Adaptive Sampling The Improved Estimators Forms of Adaptive Sampling Frame Free Adaptive Designs Sampling Without Replacement of Clusters Chapter Three - Model Assisted Adaptive Cluster Sampling Introduction Proposed Model Assist...

ABSTRACT Computing square roots over finite fields is a problem of interest, especially to understanding which algorithm is efficient, and how it works well. There are several known algorithms that computes square roots over finite fields, of all of them the shank’s algorithm is known to be the most efficient. The objective of this dissertation is to survey the square root computing algorithms over finite fields, particularly we consider the the Shank’s algorithm for computing square roo...

ABSTRACT In this thesis we shall be dealing with some basic known approximated solution of model problems involving Navier-stoke equations for incompressible fluid as well as linear elasticity theory.these include well known poiseuilleflow, Couette flow, flow between concentric cylinders, boundary layer flow over impulsively stated plate,simply supported beam with uniform distributed load, cantilevered beam with uniformly distributed load,linear membrane problems, where also an integro-diffe...

ABSTRACT Present work is concerned with solved a coefficient inverse problem of one-dimensional parabolic equation by a higher-order compact finite difference method and we used this a fourth order efficient numerical method to calculate the function u(x, t) and the unknown coefficient a(t) in a parabolic partial differential equation. Also discussed the accuracy and efficiency of the fourth order finite difference formula compare with other finite difference methods such as FTCS explicit sc...

ABSTRACT This dissertation provides general review of Partial Differential Equations. The Finite Difference Method which uses Taylor’s Theorem for solving Partial Differential Equations and Solution of elliptic partial differential equations, it also introduces the concepts of convergence, consistency and stability of finite difference scheme, Finite Difference Method (FDM) involving direct method and Iterative method like Gauss Seidel or Gauss Seidel with Successive Over Relaxation are ap...

ABSTRACT This Thesis investigates the nature of the parastrophs and derivatives of loops both of Bol-Moufang (Extra, Moufang, Central loops) and non Bol-Moufang (Conjugacy Closed loops) type in general. Extra loops is the case study. By using Fenyves (1968, 1969) definition of Extra loops and the results of Goodaire and Robinson (1982, 1990), this work shows that the parastrophs and derivatives of an Extra loop exist. Taking into consideration Ken Kunen (1996) results, it has been establishe...

ABSTRACT The study of an inverse problem for elliptic partial differential equations has been put in place in order to provide a broad understanding to the existence of inverse problems for elliptic partial differential equations particularly Poisson’s equation. The main obective is to describe different approaches to inverse problems for elliptic partial differential equations and in particular, the factorization method. Another aim of this work is to study a certain inverse problem for a...

Abstract: The present paper deals with thermal radiation eects on the transient hydro-magnetic natural convection ow past a vertical plate embedded in a porous medium with mass diusion and uctuating temperature about time at the plate, by taking account the heat due to viscous dissipation in the presence of chemical reaction. The governing equations are solved numerically by Ritz nite element method. The eects of various parameters entered into the equations of momentum, energy and concen...

ABSTRACT The purpose of this dissertation is to survey Analytic Hierarchy Process (AHP) as the tool used in decision making. The decision making process involves evaluating alternatives or criterion by selecting the best option. The AHP is the decision making technique which involves both subjective human judgments and objective evaluation merely by Eigen vector and then examines the consistency of the evaluation by Eigen Value. In this dissertation we have shown in details methods of AHP and...

ABSTRACT Over the previous years finite element method (FEM) has become a powerfully tool to approximate solution of differential equations and prove their existence. The purpose of this research is to introduce and describe a number of the finite element method (FEM) technique applied to problems for partial differential equations (PDEs) with special attentions to the hyperbolic problems in case of wave and damped wave equations. Another aim is to study the one boundary value problem (BVP) ...

ABSTRACT Partial Differential Equations (PDEs) of parabolic type arise naturally in the modeling of many phenomenon of in various fields of physics, engineering and economics. The main aim of this research is to study finite difference methods with numerical solutions of this class of equations. Both one and two dimensions have discussed in this research. I have investigated stability and convergence analysis of different schemes and obtained convergence error estimates. It is important to n...