A note on the spectra and pseudospectra of waveform relaxation operators for linear differential-algebraic equations

摘要

In this note, we derived the expressions of the spectra and pseudospectra of waveform relaxation operators for general linear differential-algebraic equations of index one. The expressions are generalizations of those of Lumsdaine and Wu (SIAM J. Sci. Comput., 18 (1997), pp. 286-304) and the derivation here is nontrivial. Numerical experiments are given to verify the theoretical results. [References: 19]