Subbarayan quadrilateral regions 11 1 1 1 1 f det

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Unformatted text preview: = ⎢ 8 ⎣ 2 19 ⎥ ⎦ Chapter 27 Page 9 G. Subbarayan Gauss-Legendre Quadrature Replace 1 n ∫ g (ξ )dξ = ∑ g (ξ −1 j =1 j )W j n sampling points – (2n-1) order polynomial can integrated exactly Chapter 27 Page 10 G. Subbarayan Chapter 27 Page 11 G. Subbarayan Quadrature Points and Weights 1 n ∫ g (ξ )dξ = ∑ g (ξ −1 j =1 j )W j 1 (a0 + a1ξ + a2ξ 2 + a3ξ 3 )dξ = W1 (a0 + a1ξ1 + a2ξ12 + a3ξ13 ) ∫ −1 +W2 (a0 + a1ξ 2 + a2ξ 22 + a3ξ 23 ) 2 2a0 + a2 = (W1 + W2 )a0 + (W1ξ1 + W2ξ 2 )a1 + ... 3 ⇒ W1 = W2 = 1 1 ξ1 = −ξ 2 = 3 Chapter 27 Page 12 G. Subbarayan Location and Weights Chapter 27 Page 13 G. Subbaraya...
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This document was uploaded on 01/29/2014.

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