Families of embedded methods of order six

Authors

  • Igor V. Olemskoy St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation https://orcid.org/0000-0001-8897-9898
  • Oxana S. Firyulina St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
  • Oleg A. Tumka St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/11701/spbu10.2022.209

Abstract

In the paper embedded methods of order six, with seven stages for solving systems of ordinary differential equations, are derived. A family of Runge — Kutta methods, of order six with seven stages and having three free parameters, is presented. This family is extended in two different ways with embedded methods to form families of embedded method pairs. Numerical comparison is given for certain examples of the embedded pairs from the constructed families.

Keywords:

Cauchy problem, embedded methods, error control, order, stage, order conditions, simplifying conditions

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Published

2022-07-28

How to Cite

Olemskoy, I. V., Firyulina, O. S., & Tumka, O. A. (2022). Families of embedded methods of order six. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 18(2), 285–296. https://doi.org/10.21638/11701/spbu10.2022.209

Issue

Vol. 18 No. 2 (2022)

Section

Control Processes

License

Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.