Publication

Abstract : This paper first presents a Gauss Legendre quadrature rule for the evaluation of View the MathML source, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)|0⩽x,y⩽1,x+y⩽1} in the two space (x,y). We transform this integral into an equivalent integral View the MathML source where S is the 2-square in (ξ, η ) space: {(ξ,η)|-1⩽ξ,η⩽1}. We then apply the one-dimensional Gauss Legendre quadrature rules in ξ and η variables to arrive at an efficient Quadrature rules with new weight coefficients and new sampling points. Then a second Gauss Legendre quadrature rule of composite type is obtained. This rule is derived by discretising T into three new triangles View the MathML source of equal size which are obtained by joining centroid of T , C=(1/3,1/3) to the three vertices of T . By use of affine transformations defined over each View the MathML source and the linearity property of integrals leads to the result: