Abstract
A simplifying assumption is introduced for general linear methods
which forces the characteristic polynomial for the stability matrix
to have the special form w^{r-1}(w - R(z)). The rational function
R(z) has a similar role to the stability function of a Runge-Kutta
method. This property, which is named "inherent RK stability"
is useful in the derivation of methods for both stiff and nonstiff
problems. We will consider the derivation of these methods by
introducing certain relationships between the four coefficent matrices
which characterize a general linear method. Unlike the more restrticted
class of DIMSIM methods, the new methods can generally be derived using
only rational operations.
This is joint work with W. M. Wright.
