Open AccessRegions of Absolute Stability
Author(s) -
Jørgen Sand,
Ole Østerby
Publication year - 1979
Publication title -
daimi pb
Language(s) - English
Resource type - Journals
eISSN - 2245-9316
pISSN - 0105-8517
DOI - 10.7146/dpb.v8i102.6518
Subject(s) - padé approximant , mathematics , stability (learning theory) , ordinary differential equation , class (philosophy) , exponential function , differential equation , differential (mechanical device) , mathematical analysis , calculus (dental) , computer science , physics , thermodynamics , medicine , dentistry , machine learning , artificial intelligence
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.