An explicit one-step multischeme sixth order method for systems of special structure

Alexey S. Eremin, Nikolai A. Kovrizhnykh, Igor V. Olemskoy

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Structure based partitioning of a system of ordinary differential equations is considered. A general form of the explicit multischeme Runge–Kutta type method for such systems is presented. Order conditions and simplifying conditions are written down. An algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given. It embeds a fourth order error estimator. Numerical comparison to the Dormand–Prince method with the same computation cost but of lower order is performed.

LanguageEnglish
Pages853-864
Number of pages12
JournalApplied Mathematics and Computation
Volume347
DOIs
StatePublished - 15 Apr 2019

Keywords

  • Explicit Runge–Kutta
  • Multischeme methods
  • Order conditions
  • Partitioned methods
  • Structural partitioning

Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

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abstract = "Structure based partitioning of a system of ordinary differential equations is considered. A general form of the explicit multischeme Runge–Kutta type method for such systems is presented. Order conditions and simplifying conditions are written down. An algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given. It embeds a fourth order error estimator. Numerical comparison to the Dormand–Prince method with the same computation cost but of lower order is performed.",
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An explicit one-step multischeme sixth order method for systems of special structure. / Eremin, Alexey S.; Kovrizhnykh, Nikolai A.; Olemskoy, Igor V.

In: Applied Mathematics and Computation, Vol. 347, 15.04.2019, p. 853-864.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Kovrizhnykh, Nikolai A.

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AB - Structure based partitioning of a system of ordinary differential equations is considered. A general form of the explicit multischeme Runge–Kutta type method for such systems is presented. Order conditions and simplifying conditions are written down. An algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given. It embeds a fourth order error estimator. Numerical comparison to the Dormand–Prince method with the same computation cost but of lower order is performed.

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