In this section, we provide a short list of some possible avenues of future research in the area of numerical integration using wave and scattering methods; several of these topics will be presented in technical detail. (Although this is perhaps not the place for such a treatment, we will do so because this material of a speculative character, and a bit too general in scope to appear in the main chapters.) Some of the more promising directions are discussed in the appendices, namely applications to fluid dynamics systems (see Appendix B), and especially, the spectral analysis of digital waveguide networks for the wave equation (see Appendix A).

- Passivity vs. Stability
- Higher-order Accuracy
- MDKC Modeling of Boundaries
- Multi-grid Methods Using MDKCs
- Spectral Mappings and Network Transformations
- Finite Arithmetic Testing
- Time-varying Systems

Stefan Bilbao 2002-01-22