Moving Boundary Value Problems

Abstract

This thesis describes new techniques of some methods which were employed to compute approximate solutions to partial differential equations with moving boundaries. The problems concerned were the determination of the concentration of oxygen diffusion in absorbing medium or tissue in both one dimensional cartesian and axially symmetric cylindrical coordinates, and the determination of the temperature in melting ice for one dimensional problem. The diffusion problem had a singularity on the initial boundary which was treated by using an approximate analytical solution and the numerical solution found by an explicit finite difference formulation of the governing differential equation for one dimensional problem, with unequal intervals in the neighbourhood of the moving boundary. A Taylor series expansion was used to solve for the oxygen concentration and to locate the boundary. For the melting ice problem the methods studied included variable time step methods with difference formulae and different methods of calculating the variable time step.