Construction of general linear methods with
Runge--Kutta stability properties
Abstract
We describe the construction of explicit general linear methods of
order p and stage order q=p with s=p+1 stages which achieve
good balance between accuracy and stability properties.
The conditions are imposed on the coefficients of these
methods which ensure that the resulting stability matrix
has only one nonzero eigenvalue. This eigenvalue depends
on one real parameter which is related to the error constant
of the method. Examples of methods are derived which
illustrate the application of the approach presented in
this talk (This is a joint work with J.C. Butcher, The University
of Auckland, New Zealand).
