An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals
The approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and fourth kinds of Chebyshev polynomials. Error esti...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/387246 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850175521474740224 |
|---|---|
| author | Sirajo Lawan Bichi Z. K. Eshkuvatov N. M. A. Nik Long |
| author_facet | Sirajo Lawan Bichi Z. K. Eshkuvatov N. M. A. Nik Long |
| author_sort | Sirajo Lawan Bichi |
| collection | DOAJ |
| description | The approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and fourth kinds of Chebyshev polynomials. Error estimates for the semibounded solutions are obtained in the class of h(t)∈CN,α[-1,1]. Numerical results for the obtained quadrature schemes revealed that the proposed methods are highly accurate when the density function h (t) is any polynomial or rational functions. The results are in line with the theoretical findings. |
| format | Article |
| id | doaj-art-bfce90e4a9454f44b7b23bd717dd55b7 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bfce90e4a9454f44b7b23bd717dd55b72025-08-20T02:19:26ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/387246387246An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular IntegralsSirajo Lawan Bichi0Z. K. Eshkuvatov1N. M. A. Nik Long2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, Selangor, MalaysiaThe approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and fourth kinds of Chebyshev polynomials. Error estimates for the semibounded solutions are obtained in the class of h(t)∈CN,α[-1,1]. Numerical results for the obtained quadrature schemes revealed that the proposed methods are highly accurate when the density function h (t) is any polynomial or rational functions. The results are in line with the theoretical findings.http://dx.doi.org/10.1155/2014/387246 |
| spellingShingle | Sirajo Lawan Bichi Z. K. Eshkuvatov N. M. A. Nik Long An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals Abstract and Applied Analysis |
| title | An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals |
| title_full | An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals |
| title_fullStr | An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals |
| title_full_unstemmed | An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals |
| title_short | An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals |
| title_sort | automatic quadrature schemes and error estimates for semibounded weighted hadamard type hypersingular integrals |
| url | http://dx.doi.org/10.1155/2014/387246 |
| work_keys_str_mv | AT sirajolawanbichi anautomaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals AT zkeshkuvatov anautomaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals AT nmaniklong anautomaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals AT sirajolawanbichi automaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals AT zkeshkuvatov automaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals AT nmaniklong automaticquadratureschemesanderrorestimatesforsemiboundedweightedhadamardtypehypersingularintegrals |