Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules

Authors

  • M. A. Hossain Jagannath University
  • M. S. Islam University of Dhaka

DOI:

https://doi.org/10.3329/jsr.v2i3.5123

Keywords:

Double integral, Numerical Integration, Quadrilateral and Triangular Finite Element, Gauss-Radau and Gauss-Lobatto quadratures.

Abstract

In this paper, numerical integrals over an arbitrary triangular region are evaluated exploiting finite element method. The physical region is transformed into a standard triangular finite element using the basis functions in local space. Then the standard triangle is discretized into 4×n2 right isosceles triangles, in which each of these triangles having area 1/2n2, and thus composite numerical integration is employed. In addition, the affine transformation over each discretized triangle and the use of linearity property of integrals are applied. Finally, each isosceles triangle is transformed into a 2-sqare finite element to generate new  n2 extended sampling points and corresponding weight coefficients, using n point’s conventional Gauss-Radau and Gauss-Lobatto quadratures, which are applied again to evaluate the double integral. The performance is depicted by means of numerical examples.

 

Keywords: Double integral; Numerical Integration; Quadrilateral and Triangular Finite Element; Gauss-Radau and Gauss-Lobatto quadratures.

 

© 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

 

DOI: 10.3329/jsr.v2i3.5123                 J. Sci. Res. 2 (3), 465-467 (2010)

 

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Author Biographies

M. A. Hossain, Jagannath University

Lecturer
Department of Mathematics
Jagannath University
Dhaka-1100,
Bangladesh

M. S. Islam, University of Dhaka

Professor

Department of Mathematics

University of Dhaka

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Published

2010-08-23

How to Cite

Hossain, M. A., & Islam, M. S. (2010). Applications of Composite Numerical Integrations Using Gauss-Radau and Gauss-Lobatto Quadrature Rules. Journal of Scientific Research, 2(3), 465. https://doi.org/10.3329/jsr.v2i3.5123

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Section

Section A: Physical and Mathematical Sciences