This report describes a high level implementation of Schwarz splitting, an approach to solving partial differential equations which seems particularly attractive from the point of view of parallelism. We discuss the basic scheme of Schwarz splitting and an implementation using ELLPACK. We consider two numerical examples in detail. The appendices contain a listing of an ELLPACK program which implements Schwarz splitting, and a complete set of data from the two examples. The examples were done on a sequential machine, but they provide clues as to the potential for parallelism exhibited by the Schwarz technique.