Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
Continuous Extensions for Structural Runge–Kutta Methods. / Eremin, A. S.; Kovrizhnykh, N. A.
Computational Science and Its Applications – ICCSA 2017: 17th International Conference, Trieste, Italy, July 3-6, 2017, Proceedings, Part II. Cham : Springer Nature, 2017. p. 363-378 (Lecture Notes in Computer Science; Vol. 10405).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review
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TY - GEN
T1 - Continuous Extensions for Structural Runge–Kutta Methods
AU - Eremin, A. S.
AU - Kovrizhnykh, N. A.
N1 - Conference code: 17
PY - 2017
Y1 - 2017
N2 - The so-called structural methods for systems of partitioned ordinary differential equations studied by Olemskoy are considered. An ODE system partitioning is based on special structure of right-hand side dependencies on the unknown functions. The methods are generalization of Runge–Kutta–Nyström methods and as the latter are more efficient than classical Runge–Kutta schemes for a wide range of systems. Polynomial interpolants for structural methods that can be used for dense output and in standard approach to solve delay differential equations are constructed. The proposed methods take fewer stages than the existing most general continuous Runge–Kutta methods. The orders of the constructed methods are checked with constant step integration of test delay differential equations. Also the global error to computational costs ratios are compared for new and known methods by solving the problems with variable time-step.
AB - The so-called structural methods for systems of partitioned ordinary differential equations studied by Olemskoy are considered. An ODE system partitioning is based on special structure of right-hand side dependencies on the unknown functions. The methods are generalization of Runge–Kutta–Nyström methods and as the latter are more efficient than classical Runge–Kutta schemes for a wide range of systems. Polynomial interpolants for structural methods that can be used for dense output and in standard approach to solve delay differential equations are constructed. The proposed methods take fewer stages than the existing most general continuous Runge–Kutta methods. The orders of the constructed methods are checked with constant step integration of test delay differential equations. Also the global error to computational costs ratios are compared for new and known methods by solving the problems with variable time-step.
KW - Continuous methods
KW - Delay differential equations
KW - Runge–Kutta methods
KW - Structural partitioning
U2 - 10.1007/978-3-319-62395-5_25
DO - 10.1007/978-3-319-62395-5_25
M3 - Conference contribution
SN - 978-3-319-62394-8
T3 - Lecture Notes in Computer Science
SP - 363
EP - 378
BT - Computational Science and Its Applications – ICCSA 2017
PB - Springer Nature
CY - Cham
T2 - 17th International Conference on Computational Science and Its Applications, ICCSA 2017
Y2 - 2 July 2017 through 5 July 2017
ER -
ID: 71300676