Abstract
A new algorithm is presented for automatic stability investigation according to the theory of Gustafsson, Kreiss and Sundstrom. It is more efficient than approaches tried earlier, by taking advantage of the special structure of the system of algebraic equations whose solutions govern stability.The software system IBSTAB implements this algorithm, as well as procedures for checking von Neumann- and P-stability. IBSTAB combines symbolic formula manipulation and numerical routines. Furthermore, a user oriented problem description language is included. The software system is entirely FORTRAN based, the symbol manipulation parts being written in LISP, using the FORTRAN coded LISP-F3 interpreter.Results are presented from tests, in which IBSTAB was addressed to problems with known results. Also, a study is presented, in which IBSTAB was used as a tool in the development of stable numerical boundary conditions for a problem in fluid dynamics.
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