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Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters
Applications of Mathematics, Tome 27 (1982) no. 4, pp. 259-276
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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.
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.
DOI : 10.21136/AM.1982.103971
Classification : 65L05, 65L20
Keywords: explicit Runge-Kutta methods; ARK methods; S-stable; LS-stable 
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Huťa, Anton; Strehmel, Karl. Construction of explicit and generalized Runge-Kutta formulas of arbitrary order with rational parameters. Applications of Mathematics, Tome 27 (1982) no. 4, pp. 259-276. doi: 10.21136/AM.1982.103971

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