Ch.H. Bischof, B. Lang, Wolfgang Marquardt, Martin Mönnigmann:
Verified determination of singularities in chemical processes
In: W. Krämer, J.W. v. Gudenberg (Eds.): SCAN 2000, 9th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, 305-317
Understanding and controlling the behavior of chemical processes are important issues, for safety as well as economical reasons. Some processes can have multiple steady states and even switch between them in a complex way, the reasons for the multiplicity not always being well understood. A singularity theory approach for investigating such behavior leads to nonlinear systems whose solutions correspond to specific singular states of the process. In order to exclude certain types of singularities, rigorous methods must be used to check the solvability of the matching systems. As these systems are highly structured, our solution method combines a symbolic preprocessing phase (term manipulation for utilizing the structure) with a branch--and--bound type rigorous interval-based solver. We report on our experience with this approach for small--to--medium sized example problems.
Chemical processes, bifurcation theory, nonlinear systems, rigorous solvers.