Numerical Methods for Stiff, Quadratic and Josephson Interferometer Differential Equations.
Abstract
THE TWO-PARAMETER CLASS OF ALL A-contractive two-step second-order formulas was derived for arbitrary step ratios. Similarly, the one-parameter class of all A-constractive two-step second-order formulas was derived for arbitrary step ratios. A specific A-contractive formula was derived which minimizes a measure of the global truncation error. The one-leg implementation of the S-contractive formulas provides A-stable methods for x = Lambda(t)x for any Lambda(t), Re Lambda(t) < or = 0 and any step sequence (hn). It was shown that, among all A-stable two-step second-order formulas for uniform steps, the A-constractive formulas are the only ones for which A-stability is conserved under any sufficiently small perturbation of the uniformity of the steps. An efficient numerical study, as well as perturbation analysis of the solutions to the two-junction interferometer was carried out.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 1980
- Accession Number
- ADA111503
Entities
People
- F. Odeh
- W. Liniger
Organizations
- IBM Thomas J. Watson Research Center