IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p738-d1349102.html
   My bibliography  Save this article

Weighted Optimal Formulas for Approximate Integration

Author

Listed:
  • Kholmat Shadimetov

    (Department of Informatics and Computer Graphics, Tashkent State Transport University, 1 Odilkhodjayev Str., Tashkent 100167, Uzbekistan
    Computational Mathematics Laboratory, V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9 University Str., Tashkent 100174, Uzbekistan)

  • Ikrom Jalolov

    (Department of Informatics and Computer Graphics, Tashkent State Transport University, 1 Odilkhodjayev Str., Tashkent 100167, Uzbekistan)

Abstract

Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the current work, we consider a discrete analogue of the differential operator 1 − 1 2 π 2 d 2 d x 2 m in the Hilbert space H 2 μ R , called D m β . We modify the Sobolev algorithm to construct optimal quadrature formulas using a discrete operator. We provide a weighted optimal quadrature formula, using this algorithm for the case where m = 1 . Finally, we construct an optimal quadrature formula in the Hilbert space H 2 μ R for the weight functions p x = 1 and p x = e 2 π i ω x when m = 1 .

Suggested Citation

  • Kholmat Shadimetov & Ikrom Jalolov, 2024. "Weighted Optimal Formulas for Approximate Integration," Mathematics, MDPI, vol. 12(5), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:738-:d:1349102
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/738/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/738/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kholmat Shadimetov & Aziz Boltaev & Roman Parovik, 2023. "Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:gam:jmathe:v:12:y:2024:i:5:p:738-:d:1349102. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      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.