Abstract
This chapter presents a simple example of a type of problem encountered in a variety of applications, which include convective heat transport, vorticity transport, and oil reservoir simulation. One of the parameters in this example is constant and positive, and measures the relative strength of dispersive to convective effects. Moreover, the chapter presents a derivation of a five-point difference scheme, which combines the properties of upwinding and central differencing, using the HODIE method. This is combined with a decomposition of the solution into inner and outer components to make the downstream boundary layer more manageable. The HODIE method is a systematic approach to deriving high-order difference approximations by using compact discretizations with several evaluations of the source term.
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