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

摘要

Two projects are described: (a) Stability criteria for difference approximations to hyperbolic systems, and multiplicativity of matrix norms; and (b) Problems in applied and computational linear algebra. The aim of these projects was to achieve better understanding of useful computational techniques for hyperbolic initial-boundary value problems, and to improve basic mathematical tools often used in numerical analysis and applied mathematics.