Abstract
The aim of this paper is to design a new family of numerical methods of arbitrarily high order for systems of first-order differential equations which are to be termed pseudo two-step Runge-Kutta methods. By using collocation techniques, we can obtain an arbitrarily high-order stable pseudo two-step Runge-Kutta method with any desired number of implicit stages in retaining the two-step nature. In very first investigations, the pseudo two-step Runge-Kutta methods are shown to be promising numerical integration methods.
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AMS(MOS) subject classifications (1991) 65M12 65M20
CR subject classifications G.1.7
This work was partly supported by DAAD, N.R.P.F.S. and QG-96-02
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Cong, N.H. A General Family of Pseudo Two-step Runge-Kutta Methods. SEA bull. math. 25, 61–73 (2001). https://doi.org/10.1007/s10012-001-0061-x
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DOI: https://doi.org/10.1007/s10012-001-0061-x