# Numerical Integration

(Difference between revisions)
 Revision as of 11:11, 3 November 2009 (view source)JMora (Talk | contribs)← Older edit Revision as of 11:12, 3 November 2009 (view source)JMora (Talk | contribs) (→Gauss-Legendre Numerical Integration)Newer edit → Line 15: Line 15: To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: − :$I=int_{-1}^{+1} f(\chi) d\chi$ + :$I=\int_{-1}^{+1} f(\xi) d\xi$ − + − + − + − + − + == References == == References ==

## Revision as of 11:12, 3 November 2009

Numerical integration refers to all the procedures, algorithms and techniques in the numerical analysis to obtain an approximate solution to a definite integral.

That is, how to obtain a numerical value of: $\int_{\lambda_a}^{\lambda_b}\! f(\lambda)\, d\lambda.$

where $\lambda \,$ can be a 1D, 2D or 3D domain.

For our interest in the Finite Element Method, the purpose is to describe how the element matrices can be integrated numerically.

## Gauss-Legendre Numerical Integration

To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve: $I=\int_{-1}^{+1} f(\xi) d\xi$