الصيغ التربيعية والتقريب الأفضل

Authors

  • محمد دريباتي

Abstract

نبني في هذه المقالة بعض الصيغ التربيعية المثلى, ونقوم بتطبيق تلك الصيغ لحساب قيمة تقريبية لتكامل محدد مع وزن. هذه الصيغ هي صيغ غوص – تشيبيشيف, وصيغ غوص- جاكوبي, ونثبت مبرهنة واحدة بهذا الخصوص. العقد   هي جذور الحدوديات :

 

حيث :

هي حدوديات تشيبيشيف من النوعين الأول والثاني أما  -  حدوديات جاكوبي .

 

نتعرف على التقريب الأفضل ونحصل على تقدير من الأعلى لخطأ الصيغة التربيعية بدلالة التقريب الأفضل .

كما نورد بعض الأمثلة كتطبيق للصيغ التي حصلنا عليها في حساب بعض الدوال الخاصة مثل دوال بسل   والتكاملات الناقصية .

In this paper we establish some best quadrature formulas and apply them to compute approximation value of definite integral with weight function.These formulas are Gauss – Chebyshev and Jacobi – Chebyshev formulas, we prove one theorem  in relation with this topic .

The nodes  are roots of polynomials

 

where       are Chebyshev polynomials of the first and second kind       , - Jacobi polynomials

We define the best approximation and obtain above estimation for error of quadrature formula by means of the best approximation, we also give some examples for applying to the formulas which we obtained in the calculation of some special functions like Bessel functions and elliptic integrals.

Downloads

Published

2018-12-02

How to Cite

1.
دريباتي م. الصيغ التربيعية والتقريب الأفضل. TUJ-BA [Internet]. 2018Dec.2 [cited 2025Apr.10];25(2). Available from: https://journal.tishreen.edu.sy/index.php/bassnc/article/view/4924

Issue

Vol. 25 No. 2 (2003): العلوم الأساسية

Section

Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series  

 Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series .  The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series   Publisher

 

journal uses a CC BY-NC-SA license which mean

You are free to:

  • Adapt — remix, transform, and build upon the material
  •  
  • The licensor cannot revoke these freedoms as long as you follow the license terms.

 

  • Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • NonCommercial — You may not use the material for commercial purposes.
  • ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
  • No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.