Hostname: page-component-7479d7b7d-68ccn Total loading time: 0 Render date: 2024-07-12T03:23:50.233Z Has data issue: false hasContentIssue false
  • English
  • Français

Weierstrass elliptic difference equations

Published online by Cambridge University Press:  17 April 2009

Renfrey B. Potts
Renfrey B. Potts
Affiliation:
Applied Mathematics Department, The University of Adelaide, South Australia.
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.

The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 1 , February 1987 , pp. 43 - 48
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Abramowitz, A. and Stegun, I. A., (eds.), Handbook of mathematical functions, U.S. National Bureau of Standards, Washington D.C. (1964).Google Scholar
[2]Potts, R. B., “Best difference equation approximation to Duffing's equation”, J. Austral. Math. Soc. Ser. B 23 (1982), 349–356.Google Scholar
[3]Potts, R. B., “Differential and difference equations”, Am. Math. Mon. 89 (1982), 402–407.Google Scholar
[4]Potts, R. B., “Nonlinear difference equation”, Nonlinear Anal. 6 (1982), 659–665.CrossRefGoogle Scholar
[5]Potts, R. B., “Van der Pol difference equation”, Nonlinear Anal. 7 (1983), 801–812.Google Scholar