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

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 35: Thurs, 12Nov09


Page 35-1

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Gauss Legendre quadrature (numerical integration}

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

 

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  ...

ReferencesEdit