Stability and B-convergence of general linear methods

摘要

This paper continues earlier work by the same author concerning the stability and B-convergence of general linear methods for the numerical solution of nonlinear stiff initial-value problems in a Hilbert space. In a previous paper we have proved that BH-consistency (resp. BH∗-consistency) together with BH-stability implies optimal B-convergence (resp. B-convergence). In this paper by means of BS- and BSI-stability properties the sufficient conditions for a method to be B-, BH∗, BH-, or BH∗-consistent, BH- or weakly BH-stable, B- or optimally B-convergent, respectively, are further established.