J. Álvarez and J.
Rojo
An improved class of generalized
Runge-Kutta methods for stiff problems. Part II: The separated system
case
Appl.
Math. Comput., 159 (2004),
pp. 717-758.
Abstract:
In order to study a generalization of the explicit $p$-stage
Runge-Kutta
methods, we introduce a new family of $p$-stage formulas for the
numerical
integration of some special systems of ODEs that provides better order
and stability results with the same number of stages. In our recent
paper
entitled 'An improved class of generalized Runge-Kutta methods for
stiff
problems. Part I: The scalar case' we studied new schemes for the
numerical
integration of scalar autonomous ODEs. In this second part we will show
that it is possible to generalize our GRK-methods so that they can be
applied
to some non-autonomous scalar ODEs and systems obtaining linearly
implicit
A-stable and L-stable methods. These methods do not require Jacobian
evaluations
in their implementation. 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 separa.pdf