Computing derivatives of Jacobi polynomials using Bernstein transformation and differentiation matrix

Abedallah Rababah; Mohammed Al-Refai; Radwan Al-Jarrah

doi:10.1080/01630560802099761

Computing derivatives of Jacobi polynomials using Bernstein transformation and differentiation matrix

Abedallah Rababah, Mohammed Al-Refai, Radwan Al-Jarrah

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n-p and Jacobi basis form of degree n-p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented.

Original language	English
Pages (from-to)	660-673
Number of pages	14
Journal	Numerical Functional Analysis and Optimization
Volume	29
Issue number	5-6
DOIs	https://doi.org/10.1080/01630560802099761
Publication status	Published - May 2008

Keywords

Basis transformation
Bernstein polynomials
Derivative evaluation
Jacobi polynomials

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

Access to Document

10.1080/01630560802099761

Cite this

@article{b2899a0661364a588e18deaa54b839d7,

title = "Computing derivatives of Jacobi polynomials using Bernstein transformation and differentiation matrix",

abstract = "In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n-p and Jacobi basis form of degree n-p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented.",

keywords = "Basis transformation, Bernstein polynomials, Derivative evaluation, Jacobi polynomials",

author = "Abedallah Rababah and Mohammed Al-Refai and Radwan Al-Jarrah",

year = "2008",

month = may,

doi = "10.1080/01630560802099761",

language = "English",

volume = "29",

pages = "660--673",

journal = "Numerical Functional Analysis and Optimization",

issn = "0163-0563",

publisher = "Taylor and Francis Ltd.",

number = "5-6",

}

TY - JOUR

T1 - Computing derivatives of Jacobi polynomials using Bernstein transformation and differentiation matrix

AU - Rababah, Abedallah

AU - Al-Refai, Mohammed

AU - Al-Jarrah, Radwan

PY - 2008/5

Y1 - 2008/5

N2 - In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n-p and Jacobi basis form of degree n-p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented.

AB - In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n-p and Jacobi basis form of degree n-p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented.

KW - Basis transformation

KW - Bernstein polynomials

KW - Derivative evaluation

KW - Jacobi polynomials

UR - http://www.scopus.com/inward/record.url?scp=45849136002&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45849136002&partnerID=8YFLogxK

U2 - 10.1080/01630560802099761

DO - 10.1080/01630560802099761

M3 - Article

AN - SCOPUS:45849136002

SN - 0163-0563

VL - 29

SP - 660

EP - 673

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

IS - 5-6

ER -

Computing derivatives of Jacobi polynomials using Bernstein transformation and differentiation matrix

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this