## Title data

Baier, Robert:

**Selection Strategies for Set-Valued Runge-Kutta Methods.**

*In:* Li, Zhilin ; Vulkov, Lubin ; Waśniewski, Jerzy
(ed.):
Numerical Analysis and Its Applications : Third International Conference, NAA 2004, Rousse, Bulgaria, June 29-July 3, 2004 ; Revised Selected Papers. -
Berlin ; Heidelberg
: Springer
,
2005
. - pp. 149-157
. - (Lecture Notes in Computer Science
; 3401
)

ISBN 978-3-540-24937-5

DOI: https://doi.org/10.1007/978-3-540-31852-1_16

Review: |

## Abstract in another language

A general framework for proving an order of convergence for set-valued Runge Kutta methods is given in the case of linear differential inclusions, if the attainable set at a given time should be approximated. The set-valued method is interpreted as a (set-valued) quadrature method with disturbed values for the fundamental solution at the nodes of the quadrature method. If the precision of the quadrature method and the order of the disturbances fit together, then an overall order of convergence could be guaranteed. The results are applied to modified Euler method to emphasize the dependence on a suitable selection strategy (one strategy leads to an order breakdown).

## Further data

Item Type: | Article in a book |
---|---|

Refereed: | Yes |

Additional notes: | Contents:
1. Introduction 2. Quadrature and Combination Methods 3. Set-Valued Runge-Kutta Methods 4. Conclusions |

Keywords: | Set-valued Runge-Kutta methods; Linear differential inclusions; Selection strategies; Modified Euler |

Subject classification: | Mathematics Subject Classification Code: 65L05 (65L06 34A30) |

Institutions of the University: | Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 02 Mar 2021 09:16 |

Last Modified: | 25 Mar 2021 06:07 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63548 |