INTEGRATION TECHNIQUES FOR TWO DIMENSIONAL DOMAINS

Logah Perumal

Abstract: In this work, three different integration techniques, which are the numerical, semi-analytical and exact integration techniques are briefly reviewed. Numerical integrations are carried out using three different Quadrature rules, which are the Classical Gauss Quadrature, Gauss Legendre and Generalized Gaussian Quadrature. Line integral method is used to perform semi-analytical integration, while the generalized equations developed by the author in previous works are used to carry out the exact integration. It is seen that Generalized Gaussian Quadrature rules outperforms other Quadrature rules during the numerical and semianalytical integrations. It is also shown that the exact integration technique developed by the author in previous works yield accurate results for integration of monomials.

Keywords: Numerical Integration, Semi-Analytical Integration, Exact Integration, Quadrature Rules, Classical Gauss Quadrature, Gauss Legendre, Generalized Gaussian Quadrature, Line Integral, and Generalized Equations

DOI: https://doi.org/10.15623/ijret.2014.0307084