The following is a list of available projects for the academic year 2008/9. Students are urged to consult the supervisors for further details about the projects.

1. Forest Model Simulation

   Suppose that we are interested in a forest that is composed of two species of trees, with x(t) and y(t) denoting the number of each species in the forest in year t. When a tree dies, a new tree grows in its place, but the new tree might be of either species. The changes in the populations of the trees in time may be modelled by a system of differential equations

   

   Solve the system of equations exactly using ordinary differentiation tech niques and numerically using the Runge-Kutta method (or any method of your choice) to illustrate what will happen to the populations over time.

   Supervisor: Dr. S.S. Motsa

2. Mathematics Modeling of the SARS epidemic

   In this project we illustrate the use of mathematical modeling techniques in modeling the spread of Severe Acute Respiratory Syndrome (SARS) in a community. A simple SIR model, described by the differential equations given below, is used to study the dynamics of  the disease.

    

   The main tasks are as follows:

   • Solve the governing equations numerically using the Runge-Kutta method.
   •  Solve the governing equations using in-built MATLAB or MAPLE differential equations solvers.
   •  Present the results graphically, analyze and interpret the results.

   Supervisor: Dr. S.S. Motsa

3. Analytical and Numerical solutions of a fluid flow over a moving surface

   This project is based on a paper that was published by Ali Chamkha in 2003. The problem under consideration is that of a fluid flowing over a permeable moving surface. The governing equations are given as

   

   The main aim of the project is to find an exact solution of the above equations and compare the solution with a finite difference numerical solution.

   Supervisor: Dr. S.S. Motsa

4. Unsteady heat conduction in a semi-infinite slab with surface convection

   Prove that the transient temperature distribution in a semi-infnite solid that is initially at a uniform temperature Ti and that has convection at the boundary surface  is given by

   

    where erfc is the complementary error function.

   Supervisor: Dr. S.S. Motsa

5. Heat transfer in a semi-in nite wall subject to periodically vary- ing surface conditions

   Solve the one dimensional heat equation

   

   subject to the boundary conditions

   

   and the initial condition

   

   using

   • Laplace Transforms (or any other method)
   • Finite Differences

   Supervisor: Dr. S.S. Motsa