# Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters

Aplikace matematiky (1982)

- Volume: 27, Issue: 4, page 259-276
- ISSN: 0862-7940

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topHuťa, Anton, and Strehmel, Karl. "Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters." Aplikace matematiky 27.4 (1982): 259-276. <http://eudml.org/doc/15247>.

@article{Huťa1982,

abstract = {In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of suitable symbols enables the authors to generalize the Runge-Kutta formulas. The starting point for the construction of adaptive R. K. method was the consistent $s$-stage R. K. formula. Finally, the S-stability of the ARK method is investigated.},

author = {Huťa, Anton, Strehmel, Karl},

journal = {Aplikace matematiky},

keywords = {explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable; explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable},

language = {eng},

number = {4},

pages = {259-276},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters},

url = {http://eudml.org/doc/15247},

volume = {27},

year = {1982},

}

TY - JOUR

AU - Huťa, Anton

AU - Strehmel, Karl

TI - Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters

JO - Aplikace matematiky

PY - 1982

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 27

IS - 4

SP - 259

EP - 276

AB - In the article containing the algorithm of explicit generalized Runge-Kutta formulas of arbitrary order with rational parameters two problems occuring in the solution of ordinary differential equaitions are investigated, namely the determination of rational coefficients and the derivation of the adaptive Runge-Kutta method. By introducing suitable substitutions into the nonlinear system of condition equations one obtains a system of linear equations, which has rational roots. The introduction of suitable symbols enables the authors to generalize the Runge-Kutta formulas. The starting point for the construction of adaptive R. K. method was the consistent $s$-stage R. K. formula. Finally, the S-stability of the ARK method is investigated.

LA - eng

KW - explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable; explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable

UR - http://eudml.org/doc/15247

ER -

## References

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