Runge-Kutta methods for affinely controlled nonlinear systems

Peter E. Kloeden; Andreas Rößler

doi:10.1016/j.cam.2006.02.061

Runge-Kutta methods for affinely controlled nonlinear systems

Peter E. Kloeden, Andreas Rößler^*

^*Corresponding author for this work

Institute of Mathematics

Johann Wolfgang Goethe-University

7 Citations (Scopus)

Abstract

Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge-Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grüne and Kloeden.

Original language	English
Journal	Journal of Computational and Applied Mathematics
Volume	205
Issue number	2
Pages (from-to)	957-968
Number of pages	12
ISSN	0377-0427
DOIs	https://doi.org/10.1016/j.cam.2006.02.061
Publication status	Published - 15.08.2007

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10.1016/j.cam.2006.02.061

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title = "Runge-Kutta methods for affinely controlled nonlinear systems",

abstract = "Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge-Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Gr{\"u}ne and Kloeden.",

author = "Kloeden, \{Peter E.\} and Andreas R{\"o}{\ss}ler",

year = "2007",

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TY - JOUR

T1 - Runge-Kutta methods for affinely controlled nonlinear systems

AU - Kloeden, Peter E.

AU - Rößler, Andreas

PY - 2007/8/15

Y1 - 2007/8/15

N2 - Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge-Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grüne and Kloeden.

AB - Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge-Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grüne and Kloeden.

UR - https://www.scopus.com/pages/publications/34248156698

U2 - 10.1016/j.cam.2006.02.061

DO - 10.1016/j.cam.2006.02.061

M3 - Journal articles

AN - SCOPUS:34248156698

SN - 0377-0427

VL - 205

SP - 957

EP - 968

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Runge-Kutta methods for affinely controlled nonlinear systems

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