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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)
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Abstract

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

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