IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v135y2017icp72-85.html
   My bibliography  Save this article

Complexity of parametric initial value problems for systems of ODEs

Author

Listed:
  • Daun, Thomas
  • Heinrich, Stefan

Abstract

We study the approximate solution of initial value problems for parameter dependent finite or infinite systems of scalar ordinary differential equations (ODEs). Both the deterministic and the randomized setting is considered, with input data from various smoothness classes. We study deterministic and Monte Carlo multilevel algorithms and derive convergence rates. Moreover, we prove their optimality by showing matching (in some limit cases up to logarithmic factors) lower bounds and settle this way the complexity. Comparisons between the deterministic and randomized setting are given, as well.

Suggested Citation

  • Daun, Thomas & Heinrich, Stefan, 2017. "Complexity of parametric initial value problems for systems of ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 135(C), pages 72-85.
    • Handle: RePEc:eee:matcom:v:135:y:2017:i:c:p:72-85
    DOI: 10.1016/j.matcom.2015.04.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415000713
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2015.04.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:135:y:2017:i:c:p:72-85. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.