Regions of Absolute Stability

Abstract

At the Department of Computer Science a system has been developed for plotting regions of absolute stability for a large class of formulae and methods for solving systems of ordinary differential equations. This report is a pictorial guide through the stability regions of a number of well-known formulae thereby showing the capabilities of our programs, and hopefully also giving some new information about the methods. In an appendix we give coefficients for Adams, Nystrom, generalized Milne-Simpson and backward differentiation formulae up to order 12 (resp. 11) and coefficients for Pade approximations to the exponential up to degree 6.