J. Álvarez and J. Rojo
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 experiments.
AMS(MOS) subject classification: 65L05, 65L07, 65L20 

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