## Title data

Grüne, Lars ; Kloeden, Peter E.:

**Pathwise Approximation of Random Ordinary Differential Equations.**

*In:* BIT Numerical Mathematics.
Vol. 41
(September 2001)
Issue 4
.
- pp. 711-721.

ISSN 0006-3835

DOI: https://doi.org/10.1023/A:1021995918864

## Abstract in another language

Standard error estimates for one-step numerical schemes for nonautonomous ordinary differential equations usually assume appropriate smoothness in both time and state variables and thus are not suitable for the pathwise approximation of random ordinary differential equations which are typically at most continuous or Hölder continuous in the time variable. Here it is shown that the usual higher order of convergence can be retained if one first averages the time dependence over each discretization subinterval.

## Further data

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

Refereed: | Yes |

Keywords: | Euler method; Averaging method; Error reduction; Heun methods; Random ordinary differential equation |

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) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne |

Result of work at the UBT: | No |

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

Date Deposited: | 23 Feb 2021 09:45 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63327 |