This US-Czech mathematics research project on Symbolic Derivation, Analysis, and Programming of Finite Difference Schemes is between Dr. Stanly Steinberg of the University of New Mexico and Dr. Richard Liska of the Czech Technical University, Prague. Their research effort will extend the current symbolic techniques used to study finite-difference approximations. The researchers hope to improve the existing technology for analyzing truncation errors and stability, and the algorithms for generating code. Cylindrical decomposition algorithms will be used to study a system of inequalities that arise in a Routh- Hurwitz problem obtained from the Von Neumann stability condition. Techniques for comparing finite-diffence algorithms on non-orthogonal grids will be developed. The researchers will pursue work with numerical diffusion and dispersion, group velocities, stability of boundary conditions, conservation laws, and stability analysis via the energy method. As a result of their collaboration, the researchers expect to extend the FORTRAN-code generation algorithms to a high-performance computing environment for use in study of a five- dimensional Fokker-Planck equation and the three-dimensional Navier Stokes equation. This project in mathematics fulfills the program objective of advancing scientific knowledge by enabling leading experts in the United States and Eastern Europe to combine complimentary talents and pool research resources in areas of strong mutual interest and competence.
