On Gauss-Type Quadrature Rules |
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| Authors: | M. A. Bokhari Asghar Qadir H. Al-Attas |
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| Affiliation: | 1. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran, Saudi Arabia mbokhari@kfupm.edu.sa;3. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran, Saudi Arabia;4. Center for Applied Mathematics &5. Physics , National University of Science &6. Technology , Rawalpindi, Pakistan;7. Department of Mathematics and Statistics , King Fahd University of Petroleum and Minerals , Dhahran, Saudi Arabia |
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| Abstract: | Some Gauss-type Quadrature rules over [0, 1], which involve values and/or the derivative of the integrand at 0 and/or 1, are investigated. Our work is based on the orthogonal polynomials with respect to linear weight function ω(t): = 1 ? t over [0, 1]. These polynomials are also linked with a class of recently developed “identity-type functions”. Along the lines of Golub's work, the nodes and weights of the quadrature rules are computed from Jacobi-type matrices with simple rational entries. Computational procedures for the derived rules are tested on different integrands. The proposed methods have some advantage over the respective Gauss-type rules with respect to the Gauss weight function ω(t): = 1 over [0, 1]. |
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| Keywords: | Gauss/Gauss–Radau/Gauss–Lobatto quadrature rules Hypergeometric functions Jacobi-matrix Orthogonal polynomials Three-term recurrence relation |
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