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

Authors:
Gennady Yu. Kulikov;Sergey K. Shindin
Affiliations:
School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa;School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Venue:
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Year:
2006

Citing 1
Cited 2

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Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems

Numerical Tests with Gauss-Type Nested Implicit Runge-Kutta Formulas

ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Adaptive nested implicit Runge--Kutta formulas of Gauss type

Applied Numerical Mathematics

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Abstract

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.