New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems
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 polynomia...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/456501 |
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| author | W. M. Abd-Elhameed |
| author_facet | W. M. Abd-Elhameed |
| author_sort | W. M. Abd-Elhameed |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-beee57bc1c7b47f0a5fd21461c52e80e |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-beee57bc1c7b47f0a5fd21461c52e80e2025-08-20T02:18:58ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/456501456501New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value ProblemsW. M. Abd-Elhameed0Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaThis 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.http://dx.doi.org/10.1155/2014/456501 |
| spellingShingle | W. M. Abd-Elhameed New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems The Scientific World Journal |
| title | New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems |
| title_full | New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems |
| title_fullStr | New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems |
| title_full_unstemmed | New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems |
| title_short | New Formulae for the High-Order Derivatives of Some Jacobi Polynomials: An Application to Some High-Order Boundary Value Problems |
| title_sort | new formulae for the high order derivatives of some jacobi polynomials an application to some high order boundary value problems |
| url | http://dx.doi.org/10.1155/2014/456501 |
| work_keys_str_mv | AT wmabdelhameed newformulaeforthehighorderderivativesofsomejacobipolynomialsanapplicationtosomehighorderboundaryvalueproblems |