Citation
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
Abstract
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.
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Official URL or Download Paper: http://einspem.upm.edu.my/journal/fullpaper/vol8so...
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| Publisher: | Institute for Mathematical Research, Universiti Putra Malaysia |
| Keywords: | Product integral; Romberg method; Mixed method; Error estimate |
| Depositing User: | Nabilah Mustapa |
| Date Deposited: | 04 Sep 2015 11:11 |
| Last Modified: | 04 Sep 2015 11:11 |
| URI: | http://psasir.upm.edu.my/id/eprint/39069 |
| Statistic Details: | View Download Statistic |
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