Order Stars and Linear Stability Theory

AbstractOrder stars are a powerful modern tool for the development and analysis of numerical methods. They convey important information such as order and stability in a unified framework. A package for rendering order stars becomes part of the standard distribution in the next major release ofMathematica. An introduction to the theory is provided here, set in the context of numerical methods for Ordinary Differential Equations. The implementation is discussed and examples are given to illustrate why a computer algebra system is an ideal environment for the exploration of order stars