In this paper it is proposed to compute the volume integral of certain functions whose antiderivates with respect to one of the variates (say either x or y or z) is available. Then by use of the well known Gauss Divergence theorem, it can be shown that the volume integral of such a function is expressible as sum of four integrals over the unit triangle. The present method can also evaluate the triple integrals of trivariate polynomials over an arbitrary tetrahedron as a special case. It is also demonstrated that certain integrals which are nonpolynomial functions of trivariates x, y, z can be computed by the proposed method. Then we have applied the symmetric Gauss Legendre quadrature rules to evaluate the typical integrals governed by the proposed method.
cited By (since 1996)1
K. Va Nagaraja and Rathod, H. Tb, “Symmetric Gauss Legendre quadrature rules for numerical integration over an arbitrary linear tetrahedra in Euclidean three-dimensional space”, International Journal of Mathematical Analysis, vol. 4, pp. 921-928, 2010.