Mixed method for the product integral on the infinite interval
In this note, quadrature formula is constructed for product integral on the infinite interval I(f) = ∫ w(x)f(x)dx, where w(x) is a weight function and f(x) is a smooth decaying function for x > N (large enough) and piecewise discontinuous function of the first kind on the interval a ≤ x ≤ N. For...
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| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/39069/ http://psasir.upm.edu.my/id/eprint/39069/1/39069.pdf |
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| author | Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Muminov, Z. I. Khaldjigitov, Abduvali A. |
| author_facet | Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Muminov, Z. I. Khaldjigitov, Abduvali A. |
| author_sort | Eshkuvatov, Zainidin K. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this note, quadrature formula is constructed for product integral on the infinite interval I(f) = ∫ w(x)f(x)dx, where w(x) is a weight function and f(x) is a smooth decaying function for x > N (large enough) and piecewise discontinuous function of the first kind on the interval a ≤ x ≤ N. For the approximate method we have reduced infinite interval x [a, ∞) into the interval t[0,1] and used the mixed method: Cubic Newton’s divided difference formula on [0, t3) and Romberg method on [t3,1] with equal step size, ti = t0+ih,i=0, …,n, h=1/n, where t0 = 0,tn=1. Error term is obtained for mixed method on different classes of functions. Finally, numerical examples are presented to validate the method presented. |
| first_indexed | 2025-11-15T09:44:09Z |
| format | Article |
| id | upm-39069 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:44:09Z |
| publishDate | 2014 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-390692015-09-04T11:11:38Z http://psasir.upm.edu.my/id/eprint/39069/ Mixed method for the product integral on the infinite interval Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Muminov, Z. I. Khaldjigitov, Abduvali A. In this note, quadrature formula is constructed for product integral on the infinite interval I(f) = ∫ w(x)f(x)dx, where w(x) is a weight function and f(x) is a smooth decaying function for x > N (large enough) and piecewise discontinuous function of the first kind on the interval a ≤ x ≤ N. For the approximate method we have reduced infinite interval x [a, ∞) into the interval t[0,1] and used the mixed method: Cubic Newton’s divided difference formula on [0, t3) and Romberg method on [t3,1] with equal step size, ti = t0+ih,i=0, …,n, h=1/n, where t0 = 0,tn=1. Error term is obtained for mixed method on different classes of functions. Finally, numerical examples are presented to validate the method presented. Institute for Mathematical Research, Universiti Putra Malaysia 2014-10 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/39069/1/39069.pdf Eshkuvatov, Zainidin K. and Nik Long, Nik Mohd Asri and Muminov, Z. I. and Khaldjigitov, Abduvali A. (2014) Mixed method for the product integral on the infinite interval. Malaysian Journal of Mathematical Sciences, 8 (S). pp. 71-82. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal/fullpaper/vol8soct/7.%20Zainidin.pdf |
| spellingShingle | Eshkuvatov, Zainidin K. Nik Long, Nik Mohd Asri Muminov, Z. I. Khaldjigitov, Abduvali A. Mixed method for the product integral on the infinite interval |
| title | Mixed method for the product integral on the infinite interval |
| title_full | Mixed method for the product integral on the infinite interval |
| title_fullStr | Mixed method for the product integral on the infinite interval |
| title_full_unstemmed | Mixed method for the product integral on the infinite interval |
| title_short | Mixed method for the product integral on the infinite interval |
| title_sort | mixed method for the product integral on the infinite interval |
| url | http://psasir.upm.edu.my/id/eprint/39069/ http://psasir.upm.edu.my/id/eprint/39069/ http://psasir.upm.edu.my/id/eprint/39069/1/39069.pdf |