Highly-Stable Multistep Methods for Retarded Differential Equations.
Abstract
A linear multistep method (rho, sigma) is defined to be D(A sub 0)-stable if when it is applied to the delay differential equation dy/dt(t) = mu y(t-tau) the approximate solution (y sub h)(t sub n) nears 0 as n nears infinity for all mu epsilon(o,pi/2 tau) and all stepsized h of the form h = tau/m, m a positive integer. General properties of D(A sub 0)-stable methods are derived. These properties are similar to the properties of A-stable and A(alpha)-stable methods, for example, it is proved that a k-step D(A sub 0)-stable method or order k must be implicit. As an application it is shown that the trapezoidal method is D(A sub 0)-stable. Finally, the condition that h = tau/m is dropped and the resulting methods, which the author calls GD(A sub 0)-stable methods, are studied. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1973
- Accession Number
- AD0776273
Entities
People
- Colin Walker Cryer
Organizations
- University of Wisconsin–Madison