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On a family of cheap symmetric one-step methods of order four

Kulikov, Gennady Yu; Shindin, S.K.

Lecture Notes in Computer Science , 3991 (2006), 781-785

In the paper we present a new family of one-step methods. These methods are of the Runge-Kutta type. However, they have only explicit internal stages that leads to a cheap practical implementation. On the other hand, the new methods are of classical order 4 and stage order 2 or 3. They are A-stable and symmetric.