lecture13 - Numerical Methods in Engineering ENGR 391...

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Numerical Methods in Engineering ENGR 391 Faculty of Engineering and Computer Sciences Concordia University Numerical integration – Gauss Quadrature
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Gauss Quadrature Gauss quadrature implements a strategy of positioning any two points on a curve to define a straight line that would balance the positive and negative errors. Hence the area evaluated under this straight line provides an improved estimate of the integral. Gauss quadrature the points for evaluation in an optimal spaced. [] = = n i i i x f C f Q 0 ) ( [ ] error truncation f E Quadrature formula [] [] f E f Q dx x f b a + = ) (
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Trapezoidal rule Gauss quadrature
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Gauss Quadrature The most common Gauss Quadrature: n = 2 ) ( ) ( ) ( ) ( 2 2 1 1 1 1 n n t f C t f C t f C dt t f + + + K Exact for polynomial up to and including (2n-1) For the case with n = 2, the quadrature is exact (up to) cubic polynomial (2n-1) = 2*2-1=3. ) ( ) ( ) ( 2
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lecture13 - Numerical Methods in Engineering ENGR 391...

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