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

EGM6321 - Principles of Engineering Analysis 1, Fall 2009Edit

Mtg 35: Thurs, 12Nov09

Page 35-1


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






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




Ex:   (2 point interpolation)

Eq.(3) P.31-3  


Eq.(4) P.31-3  


Page 35-3



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  ...