Stability of Numerical Methods for Ordinary Differential Equations
by
Allison Heard
The University of Auckland

The stability of a numerical method is usually tested by applying it to the test equation y'=\lambday where the real part of \lambda is negative. The numerical solution should tend to zero just as the analytical solution does. For numerical methods used with constant step size the powers of a matrix must be bounded. However, for variable step size it is necessary to bound a product of matrices. I will review approaches to bounding products of matrices from a given class and show some applications.

Date received: October 1, 2000