B. Venkatesudu

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This paper presents a Gauss Legendre quadrature method for numerical integration over the standard triangular surface: {(x, y) | 0 , 1, 1} x y x y ≤ ≤ + ≤ in the Cartesian two-dimensional (x, y) space. Mathematical transformation from (x, y) space to (ξ, η) space map the standard triangle in (x, y) space to a standard 2-square in (ξ, η) space: {(ξ, η)|–1 ≤(More)
This paper first presents a Gauss Legendre quadrature method for numerical integration of I 1⁄4 R R T f ðx; yÞdxdy, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)j0 6 x, y 6 1, x + y 6 1} in the Cartesian two dimensional (x,y) space. We then use a transformation x = x(n,g), y = y(n,g) to change the integral I(More)
This paper presents a Gaussian quadrature method for the evaluation of the triple integral ( , , ) T I f x y z d xd yd z = ∫∫∫ , where ) , , ( z y x f is an analytic function in , , x y z and T refers to the standard tetrahedral region:{( , , ) 0 , , 1, 1} x y z x y z x y z ≤ ≤ + + ≤ in three space( , , ). x y z Mathematical transformation from ( , , ) x y(More)
This paper first presents a Gauss Legendre quadrature rule for the evaluation of I 1⁄4 R R T f ðx; yÞdxdy, where f ðx; yÞ is an analytic function in x, y and T is the standard triangular surface: fðx; yÞj0 6 x; y 6 1; xþ y 6 1g in the two space ðx; yÞ. We transform this integral into an equivalent integral R R S f ðxðn; gÞ; yðn; gÞÞ oðx;yÞ oðn;gÞ dndg where(More)
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