Stability Analysis of Finite Difference Schemes for Hyperbolic Systems and Problems in Applied and Computational Linear Algebra

摘要

During the period May 1- July 29, 1988, progress was made under Grant AFOSR-88-0175 in the following two areas: 1) E. Tadmor and Goldberg managed to unify the two main stability criteria in a previous paper, Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. This is the content of a forthcoming paper, Simple stability criteria for difference approximations of hyperbolic initial boundary value problems, which is expected to appear in the Proceedings of the Second International Conference on Hyperbolic Problems; and 2) Arens of UCLA and Goldberg have made significant progress in characterizing multiplicativity factors and other multiplicativity properties of seminorms on operator algebras. This is done mainly by studying the kernels of the seminorms. It is anticipated that a preliminary manuscript will be ready by the end of the summer, 1988. (KR)