Abstract
The concepts of G-stability for linear multistep methods and B-stability for Runge-Kutta methods are combined in a unified approach to nonlinear stability for a class of methods general enough to include these as special cases. Recent work on these developments, by Kevin Burrage and the author, is reviewed and, to exemplify the new ideas and techniques, an algebraic stability analysis is presented for the backward differentiation methods of orders 1, 2 and 3.
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