Numerical Approach for Evaluation of Surface Integrals in Polygonal Domain by Gauss Legendre Quadrature and Generalized Gaussian Quadrature Method

We present a new approach for the numerical integration of arbitrary functions over polygonal region, by applying two kinds of quadrature method Gauss Legendre quadrature and Generalized Gaussian quadrature method, the polygonal region is divided into arbitrary triangles, the sides of each triangle is noted as equation of straight line by joining two end vertices, this approach is used to further reduces the integral equations, numerical integration of rational and irrational functions are approximated computationally, we illustrate several numerical examples to shows the accuracy of the present method