A New Class of Highly-Stable Methods: (A sub 0) -Stable Methods.

摘要

A linear multistep method (rho,Sigma) is defined to be (A sub 0) -stable if when it is applied to the equation x(t) =lambda x(t) the approximate solution (x sup h) (t sup n) tends to zero as (t sub n) nears infinity for all values of the stepsize h and all lambda ( o,infinity). Various properties of (A sub 0) -stable methods are derived. It is shown that most of the properties of A(alpha) -stable methods are shared by (A sub 0) -stable methods. It is proved that there exist (A sub 0) -stable methods of arbitrarily high order. (Author)