Solving Hyperbolic PDEs in Matlab

and we allow general boundary conditions. Solving PDEs of this generality is not routine and the success of our software is not assured. On the other hand, it is very easy to use and has performed well on a wide variety of problems. Explicit central finite difference methods are quite attractive for hyperbolic PDEs of this generality. We have implemented four: A two-step variant of the Lax-Friedrichs (LxF) method [8], Richtmyer’s two-step variant of the LaxWendroff (LxW) method [6], and the LxW method with a nonlinear filter [1] are available for all three forms. A variant of the Nessyahu-Tadmor (NT) method [4] is available for systems of form 3. The basic methods are generally recognized as effective, but the variants implemented have some advantages. For instance, the variant of LxF is dissipative and damps middle frequencies less than the usual scheme. The nonlinear filter can be quite helpful in dealing with the oscillations characteristic of LxW. The variant of NT is much better suited to the Matlab problem solving environment (PSE). An important part of this investigation was to devise a convenient way to deal with general boundary conditions. In the case of the NT method, little attention has been given to conditions other than periodicity, so in §4.2 we develop fully a treatment of general boundary conditions for systems of equations. To be sure, this is only one aspect of a user interface that we have crafted to make as easy as possible to use whilst still capable of solving a large class of problems.