Standard
Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. / Eremin, Alexey S.; Kovrizhnykh, Nikolai A.; Olemskoy, Igor V.
Computational Science and Its Applications – ICCSA 2019 : 19th International Conference, Saint Petersburg, Russia, July 1–4, 2019, Proceedings, Part I. ред. / Sanjay Misra; et al. Springer Nature, 2019. стр. 89-102 (Lecture Notes in Computer Science ; Том 11619 ).
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Harvard
Eremin, AS, Kovrizhnykh, NA & Olemskoy, IV 2019,
Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. в S Misra & EA (ред.),
Computational Science and Its Applications – ICCSA 2019 : 19th International Conference, Saint Petersburg, Russia, July 1–4, 2019, Proceedings, Part I. Lecture Notes in Computer Science , Том. 11619 , Springer Nature, стр. 89-102, 19th International Conference on Computational Science and Its Applications, ICCSA 2019, Saint Petersburg, Российская Федерация,
1/07/19.
https://doi.org/10.1007/978-3-030-24289-3_8
APA
Eremin, A. S., Kovrizhnykh, N. A., & Olemskoy, I. V. (2019).
Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. в S. Misra, & E. A. (Ред.),
Computational Science and Its Applications – ICCSA 2019 : 19th International Conference, Saint Petersburg, Russia, July 1–4, 2019, Proceedings, Part I (стр. 89-102). (Lecture Notes in Computer Science ; Том 11619 ). Springer Nature.
https://doi.org/10.1007/978-3-030-24289-3_8
Vancouver
Eremin AS, Kovrizhnykh NA, Olemskoy IV.
Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. в Misra S, EA, Редакторы, Computational Science and Its Applications – ICCSA 2019 : 19th International Conference, Saint Petersburg, Russia, July 1–4, 2019, Proceedings, Part I. Springer Nature. 2019. стр. 89-102. (Lecture Notes in Computer Science ).
https://doi.org/10.1007/978-3-030-24289-3_8
Author
Eremin, Alexey S. ; Kovrizhnykh, Nikolai A. ; Olemskoy, Igor V. /
Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. Computational Science and Its Applications – ICCSA 2019 : 19th International Conference, Saint Petersburg, Russia, July 1–4, 2019, Proceedings, Part I. Редактор / Sanjay Misra ; et al. Springer Nature, 2019. стр. 89-102 (Lecture Notes in Computer Science ).
BibTeX
@inproceedings{2486e79d38ea4fbcaa4e149e05df46fa,
title = "Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations",
abstract = "Structural partitioning of systems of ordinary differential equations is made on base of right-hand side dependencies on the unknown variables. It is used to construct fully explicit Runge–Kutta methods with several computational schemes applied to different parts of the system. The constructed structural methods require fewer right-hand side evaluations (stages) per step for some parts of the system than classic explicit Runge–Kutta methods of the same order. The full structural form of the system is presented, which after permutation of variables can be applied to any system of ordinary differential equation. For such structure a multischeme method is formulated and conditions of the sixth order are written down. We present simplifying conditions and reduce the system to a solvable smaller system. A particular computational scheme, that requires seven stages for a group without special structure and only six stages for other equations, is presented. Its sixth order is confirmed by a numerical convergence test.",
keywords = "explicit Runge–Kutta, Multischeme methods, Order conditions, Partitioned methods, Structural partitioning",
author = "Eremin, {Alexey S.} and Kovrizhnykh, {Nikolai A.} and Olemskoy, {Igor V.}",
note = "Eremin A.S., Kovrizhnykh N.A., Olemskoy I.V. (2019) Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations. In: Misra S. et al. (eds) Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science, vol 11619. Springer, Cham; 19th International Conference on Computational Science and Its Applications, ICCSA 2019 ; Conference date: 01-07-2019 Through 04-07-2019",
year = "2019",
month = jul,
day = "1",
doi = "10.1007/978-3-030-24289-3_8",
language = "English",
isbn = "9783030242886",
series = "Lecture Notes in Computer Science ",
publisher = "Springer Nature",
pages = "89--102",
editor = "Sanjay Misra and {et al.}",
booktitle = "Computational Science and Its Applications – ICCSA 2019",
address = "Germany",
}
RIS
TY - GEN
T1 - Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations
AU - Eremin, Alexey S.
AU - Kovrizhnykh, Nikolai A.
AU - Olemskoy, Igor V.
N1 - Conference code: 19
PY - 2019/7/1
Y1 - 2019/7/1
N2 - Structural partitioning of systems of ordinary differential equations is made on base of right-hand side dependencies on the unknown variables. It is used to construct fully explicit Runge–Kutta methods with several computational schemes applied to different parts of the system. The constructed structural methods require fewer right-hand side evaluations (stages) per step for some parts of the system than classic explicit Runge–Kutta methods of the same order. The full structural form of the system is presented, which after permutation of variables can be applied to any system of ordinary differential equation. For such structure a multischeme method is formulated and conditions of the sixth order are written down. We present simplifying conditions and reduce the system to a solvable smaller system. A particular computational scheme, that requires seven stages for a group without special structure and only six stages for other equations, is presented. Its sixth order is confirmed by a numerical convergence test.
AB - Structural partitioning of systems of ordinary differential equations is made on base of right-hand side dependencies on the unknown variables. It is used to construct fully explicit Runge–Kutta methods with several computational schemes applied to different parts of the system. The constructed structural methods require fewer right-hand side evaluations (stages) per step for some parts of the system than classic explicit Runge–Kutta methods of the same order. The full structural form of the system is presented, which after permutation of variables can be applied to any system of ordinary differential equation. For such structure a multischeme method is formulated and conditions of the sixth order are written down. We present simplifying conditions and reduce the system to a solvable smaller system. A particular computational scheme, that requires seven stages for a group without special structure and only six stages for other equations, is presented. Its sixth order is confirmed by a numerical convergence test.
KW - explicit Runge–Kutta
KW - Multischeme methods
KW - Order conditions
KW - Partitioned methods
KW - Structural partitioning
UR - http://www.scopus.com/inward/record.url?scp=85069154587&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-24289-3_8
DO - 10.1007/978-3-030-24289-3_8
M3 - Conference contribution
AN - SCOPUS:85069154587
SN - 9783030242886
T3 - Lecture Notes in Computer Science
SP - 89
EP - 102
BT - Computational Science and Its Applications – ICCSA 2019
A2 - Misra, Sanjay
A2 - null, et al.
PB - Springer Nature
T2 - 19th International Conference on Computational Science and Its Applications, ICCSA 2019
Y2 - 1 July 2019 through 4 July 2019
ER -
