Pseudospectra for matrix pencils and stability of equilibria
The \(\varepsilon\)-pseudospectra studied by \textit{N. M. Nachtigal}, \textit{S. C. Reddy} and \textit{L. N. Trefethen} [SIAM J. Matrix Anal. Appl. 13, No. 3, 778-795 (1992; Zbl 0754.65036)] are considered for matrix pencils. It is shown how the \(\varepsilon\)-pseudospectra for matrix pencils can be used to investigate the asymptotic stability of stationary solutions to systems of time-dependent ordinary or partial differential equations, when inexact Jacobian matrices are used. This approach is illustrated by the study of two systems of ordinary differential equations. Both systems are obtained from a semidiscretization of Burgers' equation, applying a finite difference and a finite element method, respectively.
scientific article; zbMATH DE number 1117810