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...
ABSTRACT We obtain new exact solutions to the Einstein field equations for anisotropic neutral stellar objects. In our dissertation, we are considering a quadratic equation of state and a choice of measure of anisotropy and metric function adopted from Sunzu’s work. We transform the Einstein field equations for neutral anisotropic matter by adopting the Durgapal and Bannerji’s new variables. We generate the exact solution and hence obtain the gravitational potentials and matter variables...
ABSTRACT This dissertation is a study of finite difference numerical methods that are based on the principle of discretization. In chapter one we present the general overview of partial differential equations, Initial boundary value problems and derivations of Finite difference methods for one dimensional heat equation. A brief discussion of the truncation error is also presented. The second chapter is concerned with consistency, stability and convergence of the finite difference schemes for...
ABSTRACT A number of phenomena in modern science can be conveniently described in terms of problems for parabolic equations with Bessel operator and nonlocal conditions. The purpose of this study is to give a survey of classical and nonclassical problems for parabolic differential equations with Bessel operator, give introduction to several different research approaches and show how the choice of a method depends on the nature of the problem. Another aim is to study the solution to the proble...
ABSTRACT Multiple choice examinations are commonly used to assess student learning. However, instructors often find it challenging to write good items that ask students to do more than memorize facts and details. Multiple choice test items are generally more complex and time-consuming to create than other types of tests. It requires a certain amount of skill. However, this skill may be increases through study, practice and experience. This dissertation discusses a number of issues related to...
ABSTRACT This study aimed at investigating the contribution of teaching aids (counting objects) in numeracy skills performance for standard two pupils. The main objective of this study was to introduce an effective intervention for enhancing pupils‟ achievement levels in numeracy. The study revealed that there is a low numeracy skill which is caused by many reasons such as unsuitable teaching and learning environment, few teaching methods, negative attitude of pupils and parents towards nu...
ABSTRACT This dissertation reviews numerical solution of parabolic partial differential equations. A short description and classification of parabolic partial differential equation is presented. The explicit, implicit and Crank-Nicolson numerical techniques are discussed in relation to consistency, convergence and stability. Analytical and numerical solutions of well-posed problem are obtained by Crank- Nicolson and Laplace transform methods, and discussed through a practical example. Simulat...
ABSTRACT This project research titled “Design and Implementation of an Online Journal Management System which is a case study of Sokoto International Journal of Counselling Psychology (SIJCP)” is a web-based system which is aimed at using the potent ability of the Computer System to solve many of the challenges faced by the current manual system of Journal and Publication processes. It provides numerous benefits which include: Automation of the Submission process, review process, payment ...
ABSTRACT We find new exact solutions to Einstein-Maxwell field equation for neutral anisotropy stellar stars with Van der Waals equation of state. We adopted Sunzu, Maharaj and Ray‘s metric function and measure of anisotropy. The solutions are obtained after considering the transformed Einstein-Maxwell field equations for neutral anisotropic matter. In our models, we regain previous anisotropic and isotropic results as a special case. We consider the space-time geometry to be static spheric...
Abstract In this dissertation, we generate solutions to Einstein-Maxwell field equations devoted to neutral anisotropic stellar objects using linear equation of state. The field equations are transformed by adopting Bannerji and Durgapal transformation. We generated the solutions to Einstein field equations and obtain matter variables and gravitational potentials by using the general differential equation governing the model. In our model, isotropic results are regained as a special case. Th...
ABSTRACT In this study we find the conditions of mass function for the formation and existence of naked singularity of the metric given in generalized Vaidya spacetime. We study and clarify how naked singularity is brought about interms of the apparent and event horizon. We analyse the components of the metric as given in the Vaidya spacetime equation. We consider the collapsing model in which the imploding radiation collapses at the center of symmetry in the universe through which we derive...
ABSTRACT Numeracy education is a very important component in human life activities and survival. It is useful in science, technology, commerce, economics, and education. The purpose of the study was to investigate the teacher factors affecting performance of standard two pupil‟s in numeracy skills in public primary schools in Songea Municipality, Ruvuma Region. Three research objectives guided the study. The objectives sought to find out the extent to which attitudes of teachers affects th...
ABSTRACT This study is concerned with overview numerical solution for nonlinear partial dierential equations. Since it is not easily to iterate the numerical scheme manually, C++ is used to encode the numerical scheme in order to nd the numerical solution and Matlab is employed in drawing the gures. Chapter one consists of Introduction of Nonlinear Partial Dierential equations, Literature Review, Classication of Partial Dierential Equations, Examples of PDEs, Boundary Conditions, Taylor Expan...
ABSTRACT The study of predator prey model with immigrant prey with and without harvesting has received great attention from both theoretical and mathematical biologists and has been studied intensively and extensively. Different literatures on interaction between species have been surveyed. In this document we establish sufficient stability criteria, criteria for the existence of periodic solution and Hopf bifurcations of a predator prey systems with immigrant prey without and with harvesting...