J. Álvarez and J.
Rojo
An improved class of generalized
Runge-Kutta methods for stiff problems
Technical Report, (2000)
Abstract:
A new family of explicit $p$-stage methods for the numerical integration
of scalar
autonomous ODEs is proposed. These methods can be seen as a generalization
of the explicit
$p$-stage Runge-Kutta ones, while providing better order and stability
results. In fact, we
show that it is possible to obtain A-stable and L-stable formulas of
order three and
five, with only two and three evaluations per step respectively, and
without losing
the explicitness of the formulas. It is also possible to generalize
the methods to get
formulas for some non-autonomous scalar ODEs and systems. We obtain
linearly implicit
A-stable methods which do not require Jacobian evaluations. Some numerical
examples are
discussed in order to show the good performance of the new schemes.
AMS(MOS) subject classification:
65L05, 65L07, 65L20
Preprint file as PDF improv.pdf