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.

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Published

2018-12-02

How to Cite

1.
دريباتي م. الصيغ التربيعية والتقريب الأفضل. TUJ-BA [Internet]. 2018Dec.2 [cited 2024May9];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

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