Optimal first- to sixth-order accurate Runge-Kutta schemes

Author:

Alshina E. A.,Zaks E. M.,Kalitkin N. N.

Publisher

Pleiades Publishing Ltd

Subject

Computational Mathematics

Reference6 articles.

1. E. Hairer, S. P. Nörsett, and G. Wanner, Solving Ordinary Differential Equations. I: Nonstiff Problems (Springer-Verlag, Berlin, 1987; Mir, Moscow, 1990).

2. J. C. Butchern, “Coefficients for Study of Runge-Kutta Integration Processes,” J. Austral. Math. Soc. 3, 185–201 (1963).

3. G. M. Hammud, “Three-Dimensional Family of Seven-Stage Runge-Kutta Methods of the Sixth Order,” Vychisl. Metody Program. 2(2), 71–78 (2001).

4. K. Dekker and J. G. Verwer, Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations (North-Holland, Amsterdam, 1984; Mir, Moscow, 1988).

5. G. I. Marchuk and V. V. Shaidurov, Improving the Accuracy of Finite Difference Schemes (Nauka, Moscow, 1979) [in Russian].

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