We describe the characteristics of partial differential equations (PDEs), including their uses, classification, subsidiary conditions and some of the ways in which they may be solved. In this context, we demonstrate how routines from the NAG Library can be used in their numerical solution. These routines come not only from the Library's PDE chapter, but also from the chapters that deal with mesh generation and the solution of large linear systems. The combination of mesh generators and large linear solvers is applicable in the implementation of the so-called finite element method, which may be used in cases where the complexity of the geometry of the domain over which the PDE is to be solved prevents the application of the comparatively simple finite differencing method (as used, for example, in the Library's PDE chapter).

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