ABSTRACT
So far in this book the schemes that have been developed to solve partial
differential equations (PDEs) such as the transport, heat or convection equation
have been derived in such a way that there is a single unknown in each equation.
These explicit schemes are easy to code and implement, but there are other ways of
tackling the problem. Firstly, there are other ways of constructing the individual
approximations that lead to different explicit schemes. Secondly, there are schemes
that can be developed where each equation contains more than one unknown. These
schemes, which are called implicit, require a matrix solution for their
implementation. This adds a level of complication for the programmer but there are
significant advantages with this approach.
