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 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...
Abstract This paper concentrates on the mathematical model for optimal control and cost-effectiveness analysis of tomato yellow leaf curl virus disease. The boundedness of the model has been analytically examined. The preferable optimal level of the intervention strategy to reduce the spreads and the cost of implementing control strategies were determined by introducing the time-dependent control. Pontryagin’s maximum principle was used to determine necessary conditions for the optimal cont...
ABSTRACT A number of phenomena in modern science can be conveniently described in terms of problem for hyperbolic equation with Carleman estimates to the solution of inverse problem. The purpose of this study is to give a survey of the solution of the inverse problems for hyperbolic equation by Carleman estimates. We extend the results and prove the Carleman estimate focusing on an inverse problem for a simple hyperbolic equation. Also we derive the Lipschitz's stability by energy estimate; w...
ABSTRACT This dissertation investigates the magnetic field and Soret influence on MHD unsteady free convection radiating and reacting fluid past an exponentially accelerated inclined infinite porous plate of uniform permeability with variable temperature and concentration numerically. In this model the fluid is considered a gray, emitting absorbing radiation but a non-scattering medium and a magnetic field of intensity B0 is imposed in the perpendicular direction to the plate. The governing e...
ABSTRACT We find new exact solutions to Einstein-Maxwell's field equation for charged anisotropic stellar objects. We use the linear equations of the state consistent with quark matter and metric function. In our model, we choose a new measure of anisotropy. Through the transformation of Einstein-Maxwell field equations, new solutions for charged anisotropic matter are obtained. The models generated enable us to regain previous isotropic and anisotropic results as a specific case. We regain ...
Abstract In this paper, the effects of chemical reaction on unsteady MHD flow of viscous incompressible electrically conducting fluid past an impulsively started oscillating vertical plate with variable temperature and constant mass diffusion in the presence of Hall current have been presented. The dimensionless governing partial differential equations of the flow have been solved numerically by using the Crank-Nicolson implicit finite difference scheme. The numerical solutions for primary fl...
ABSTRACT This dissertation contains materials on numerical solutions to partial differential equations only appropriate for senior level undergraduate. 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 the name numerical methods. We shall see how...
ABSTRACT The objective of this study is to investigate the effects of chemical reaction on an unsteady hydro - magnetic natural convection heat and mass transfer flow of incompressible, viscous, rotating and radiating fluid past an infinite vertical porous flat plate in the presence of heat sink. The Rosseland approximation is used to describe the radiative heat flux for optically thick fluid in the energy equation. The system of non - dimensional partial differential equations governing the...
ABSTRACT This dissertation consists of four chapters. The first chapter is about general review of partial differential equations. The second chapter is devoted to the numerical solutions of partial differential equations. The third chapter is about applications of partial differential equations in mathematical physics and the fourth chapter is about mathematical modeling with partial differential equations.