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 -