Accession Number : AD0776273

Title :   Highly-Stable Multistep Methods for Retarded Differential Equations.

Descriptive Note : Technical rept.,

Corporate Author : WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES

Personal Author(s) : Cryer,Colin W.

Report Date : SEP 1973

Pagination or Media Count : 34

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)

Descriptors :   *Differential equations, Numerical analysis, Theorems, Time lag theory

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE