Numerical analysis of a linear continuous dynamic system with application to flood routing.

This research analyses numerically a hydrological model of a physical problem known technically as flood routing. The mathematical model of this physical problem takes the form of an initial value problem involving a system of first order differential equations. In the hydrological literature, a certain linear constant coefficient problem modelling flood routing has been discretised. The process of discretisation used lacks mathematical rigour. In this thesis we discuss the shortcomings of the standard numerical techniques. We give and analyse a new approach of deriving the known discretised schemes, involving the technique of exponential fitting. This technique is extended to cover more general problems.