Publication Type:

Journal Article

Source:

International Journal of Computer Mathematics, Volume 89, Number 12, p.1631-1640 (2012)

URL:

http://www.scopus.com/inward/record.url?eid=2-s2.0-84864065346&partnerID=40&md5=5b03021e53206985a4a9e068287f414e

Abstract:

<p>This paper presents a generalized Gaussian quadrature method for numerical integration over regions with parabolic edges. Any region represented by R 1={(x, y)| a≤x≤b, f(x) ≤y≤g(x)} or R2={(x, y)| a≤y≤b, f(y) ≤x≤g(y)}, where f(x), g(x), f(y) and g(y) are quadratic functions, is a region bounded by two parabolic arcs or a triangular or a rectangular region with two parabolic edges. Using transformation of variables, a general formula for integration over the above-mentioned regions is provided. A numerical method is also illustrated to show how to apply this formula for other regions with more number of linear and parabolic sides. The method can be used to integrate a wide class of functions including smooth functions and functions with end-point singularities, over any two-dimensional region, bounded by linear and parabolic edges. Finally, the computational efficiency of the derived formulae is demonstrated through several numerical examples. © 2012 Copyright Taylor and Francis Group, LLC.</p>

Notes:

cited By (since 1996)0

Cite this Research Publication

Dr. K.V. Nagaraja and Sarada Jayan, “Generalized Gaussian quadrature rules over regions with parabolic edges”, International Journal of Computer Mathematics, vol. 89, pp. 1631-1640, 2012.

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