(untitled) (International Journal of Engineering and Computer Science, 2017)
This paper presents a numerical integration formula for the evaluation of , where and is any polygonal domain in That is a domain with boundary composed of piecewise straight lines.We then express in which is a polygonal domain of N oriented edges with end points and . We have also assumed that can be discretised into a set of M triangles, and each triangle is further discretised into three special quadrilaterals which are obtained by joining the centroid to the midpoint of its sides. We choose an arbitrary triangle with vertices in Cartesian space We have shown that an efficient formula for this purpose is given by where, u= u(ξ,η)=(1-ξ)(5+η)/24,v=v(ξ,η)=(1-η)(5+ξ)/24 and is the standard 2 square in space. This 2 square S in is discritised into four 1squares in (ξ,η) space.We then use four linear transformations sing the Gauss Legendre Quadrature Rules of order 5(5)40, we obtain the weight coefficients and sampling points which can be used for any polygonal domain, or or (m=3n-2,3n-1,3n;b=1,2,3,4) The present composite integration scheme integrates gives the same accuracy for half the number of triangles for each discretisation of a polygon used in our earlier work[16].