University of Florida/Egm6321/F10.TEAM1.WILKS/Mtg35

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

Mtg 35: Thurs, 12Nov09


Page 35-1

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Gauss Legendre quadrature (numerical integration}

Quadrature; QUAD-->quadrilateral-->Greek: measuring areas

EGM6321 F10 TEAM1 WILKS xc mtg35 1.svg

Area Quadrilaterals

Cubature; CUBE; Volume cubes



with the roots for , where n is the degree of and being the weight


Page 35-2

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(1)



(2)

where j=1,2,...,n

(3)

for

Ex: (2 point interpolation)

Eq.(3) P.31-3



Eq.(4) P.31-3


Page 35-3

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HW: verify table for Gauss Legendre quadrature in wikipedia, analytical expression of and and (n=integration points) after verifying the expression for with ; (see HW p31-3 )

Evaluate numerically and and compute results with Abram & Stegum (see lecture plan)

Question: How does Gauss Legendre quadrature compare to other quadrature methods, e.g. trapezoidal rule?

Answer: Look at , Eq.(3) P.35-2. Consider ...

References[edit]