J. Álvarez and  J. Rojo
New A-stable explicit two-stage methods of order three for the scalar autonomous IVP
pp. 57-66 in
P. de Oliveira, F. Oliveira, F. Patrício, J.A. Ferreira, A. Araújo (eds.)
Proc. of the 2nd. Meeting on Numerical Methods for Differential Equations, NMDE'98
Coimbra, Portugal, 1998

We investigate a new family of explicit two--stage methods for the numerical integration of scalar autonomous ODEs. We show that it is possible to obtain formulae of order three with only two evaluations per step. Moreover, we can obtain A--stable and L--stable methods of order three from the preceding family. Finally we compare the new methods with other conventional methods, to show that they perform better, carrying out some numerical experiments.
AMS(MOS) subject classification: 65L05, 65L07, 65L20

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