International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 319-334

Optimally stable fifth-order integration methods: a numerical approach

D. J. Rodabaugh1 and S. Thompson2

1Department of Mathematics, University of Missouri, Columbia 65201, Missouri, USA
2The Babcock & Wilcox Company, Nuclear Power Generation Division, Lynchburg 24505, Virginia, USA

Received 16 September 1977; Revised 19 June 1978

Copyright © 1978 D. J. Rodabaugh and S. Thompson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, the results of the first detailed and systematic study of the family of fifth order implicit linear multistep methods requiring function evaluations at four backpoints are given. Also described is a practical and efficient nonlinear optimization procedure which made it possible to locate in a precise manner the methods of this type which possess optimal ranges of relative stability in the sense-that the corresponding relative stability regions contain maximal disks centered at the origin.