A nine-parametric family of embedded methods of sixth order
DOI:
https://doi.org/10.21638/11701/spbu10.2023.403Abstract
In the paper an effective explicit Runge — Kutta type method of the sixth order with an embedded error estimator of order four is presented. The method is applied to the systems that can be structurally partitioned into three subsystems. Its computational scheme effectively uses the structural properties. However this leads to much larger systems of order conditions. These nonlinear conditions and the algorithm of finding a solution with nine free parameters are presented. A certain computational scheme is written down and a numerical comparison to Dormand — Prince pairs of orders 5 and 6 is performed.
Keywords:
Runge — Kutta methods, partitioned systems, order conditions, simplifying conditions
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Eremin A. S., Kovrizhnykh N. A., Olemskoy I. V. An explicit one-step multischeme sixth order method for systems of special structure. Applied Mathematics and Computation, 2019, vol. 347, pp. 853–864.
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Olemskoy I. V., Eremin A. S. Algorithm of construction of effective explicit methods for structurally partitioned systems of ordinary differential equations. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 4, pp. 353–369. https://doi.org/10.21638/11702/spbu10.2021.404
Dormand J. R., Prince P. J. A family of embedded Runge — Kutta formulae. Journal of Computational and Applied Mathematics, 1980, vol. 6, iss. 1, pp. 19–26.
Dormand J. R., Prince P. J. High order embedded Runge — Kutta formulae. Journal of Computational and Applied Mathematics, 1981, vol. 7, iss. 1, pp. 67–75.
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