# What is Gauss Legendre equation?

## What is Gauss Legendre equation?

The Legendre-Gauss Quadrature formula or Gauss-Legendre quadrature is the numeric approximation of a definite integral, It is possible to choose quadrature points xi and weights wi, so that polynomial functions of degree smaller than 2N are integrated exactly by equation (1).

What is the degree of polynomials up to which integration of polynomial using Gauss Legendre method gives exact result?

The important property of Gauss quadrature is that it yields exact values of integrals for polynomials of degree up to 2n – 1. Gauss quadrature uses the function values evaluated at a number of interior points (hence it is an open quadrature rule) and corresponding weights to approximate the integral by a weighted sum.

### What is the relation between Legendre polynomials and Gaussian Quadrature?

The points used in Gaussian Quadrature are the roots of Pn+1, {x0,x1,…,xn}. Because of the properties of the Legendre polynomials, it turns out that if P(x) is any poly- nomial of degree k up to 2n + 1, then the Gaussian Quadrature estimate of the integral of P(x) is exact.

What is the maximum no of degree of polynomial that could be solved using Gauss quadrature method?

It is accurate for polynomials up to degree 2n – 3, where n is the number of integration points (Quarteroni, Sacco & Saleri 2000).

#### What is Gaussian Quadrature used for?

The Gaussian quadrature formula is widely used in solving problems of radiation heat transfer in direct integration of the equation of transfer of radiation over space. The application of Gauss’ formula in this case works very well especially when the number of intervals of spectrum decomposition is great.

Why is Gauss quadrature used in FEM?

Gaussian quadrature is one of the most commonly applied numerical integration methods. Gaussian quadrature approximates an integral as the weighted sum of the values of its integrand. Consider integrating the general function , over the domain − 1 ≤ ξ ≤ 1 .

## What is Gaussian quadrature used for?

What is the degree of a quadrature rule?

Definition: The degree of accuracy or precision of a quadrature formula is the largest positive integer such that the formula is exact for , for each . ∫ ; ∫ [ ] Trapezoidal rule is exact for (or ).