Hostname: page-component-745bb68f8f-s22k5 Total loading time: 0 Render date: 2025-02-05T23:51:44.455Z Has data issue: false hasContentIssue false
  • English
  • Français

Divergence of solutions of polynomial finite-difference equations

Published online by Cambridge University Press:  10 August 2012

Harry Gingold
Harry Gingold
Affiliation:
Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA (gingold@math.wvu.edu)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A theorem is proven for kth-order polynomial finite-difference equations that guarantees the divergence of solutions. A ‘basin of divergence’ is characterized and an order of divergence is provided. The basin of divergence is shown to depend on k independent parameters. An unconventional compactification method is used. Applications include the multi-step method in the numerical integration of ordinary differential equations, quadratic equations and the Henon map.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 4 , August 2012 , pp. 787 - 804
Copyright
Copyright © Royal Society of Edinburgh 2012