New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-14
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials.
The derivatives formulae for Chebyshev polynomials of third and fourth kinds of any degree and of any order in terms of their corresponding Chebyshev polynomials are deduced as special cases.
Some new reduction formulae for summing some terminating hypergeometric functions of unit argument are also deduced.
As an application, and with the aid of the new introduced derivatives formulae, an algorithm for solving special sixth-order boundary value problems are implemented with the aid of applying Galerkin method.
A numerical example is presented hoping to ascertain the validity and the applicability of the proposed algorithms.
American Psychological Association (APA)
Abd-Elhameed, W. M.. 2014. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1049676
Modern Language Association (MLA)
Abd-Elhameed, W. M.. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems. The Scientific World Journal No. 2014 (2014), pp.1-11.
https://search.emarefa.net/detail/BIM-1049676
American Medical Association (AMA)
Abd-Elhameed, W. M.. New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-11.
https://search.emarefa.net/detail/BIM-1049676
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1049676