We consider square matrices A such that ||exp(tA)||<=K for all t>=0. We show that each matrix possessing this property can be transformed to a block-diagonal form such shat condition numbers of all the digaonal blocks and the transformation matrix depend only on K and matrix size. The obtained result is applied to the analysis of long-time simulation accuracy of difference schemes.

similarity of matrices, Kreiss theorem, superconvergence, long-time simulation accuracy

Mathematical problems and theory of numerical methods

Bakhvalov Pavel Alexeevisch,  ,  orcid.org/0000-0003-3416-8277,  KIAM RAS

Surnachev Mikhail Dmitriyevich,  ,  orcid.org/0000-0003-4071-5097,  KIAM RAS