J. Álvarez and J.
A new family of explicit two-stage
methods of order three for the scalar autonomous IVP
Intl. Journal of Applied Sc. &
Computations, 5 (1999), pp. 246-251.
In this work, we propose a new family of explicit two--stage formulae
for the numerical integration of scalar autonomous ODEs. For scalar autonomous
problems, these methods can be seen as a generalization of the explicit
two--stage Runge--Kutta ones, that provides better order and stability
results. In fact, we show that it is possible to obtain formulae of order
three with only two evaluations per step. It is also possible to get A--stable
and L--stable methods of order three from the preceding family, without
losing the explicitness of the formulae. Finally we carry out some numerical
AMS(MOS) subject classification:
65L05, 65L07, 65L20
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