Reference documentation for deal.II version GIT relicensing-1062-gc06da148b8 2024-07-15 19:20:02+00:00
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QGaussChebyshev< dim > Class Template Reference

#include <deal.II/base/quadrature_lib.h>

Inheritance diagram for QGaussChebyshev< dim >:
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## Public Member Functions

QGaussChebyshev (const unsigned int n)
Generate a formula with n quadrature points.

QGaussChebyshev (const unsigned int n)

## Detailed Description

template<int dim>
class QGaussChebyshev< dim >

Gauss-Chebyshev quadrature rules integrate the weighted product $$\int_{-1}^1 f(x) w(x) dx$$ with weight given by: $$w(x) = 1/\sqrt{1-x^2}$$. The nodes and weights are known analytically, and are exact for monomials up to the order $$2n-1$$, where $$n$$ is the number of quadrature points. Here we rescale the quadrature formula so that it is defined on the interval $$[0,1]$$ instead of $$[-1,1]$$. So the quadrature formulas integrate exactly the integral $$\int_0^1 f(x) w(x) dx$$ with the weight: $$w(x) = 1/\sqrt{x(1-x)}$$. For details see: M. Abramowitz & I.A. Stegun: Handbook of Mathematical Functions, par. 25.4.38

Definition at line 558 of file quadrature_lib.h.

## ◆ QGaussChebyshev() [1/2]

template<int dim>
 QGaussChebyshev< dim >::QGaussChebyshev ( const unsigned int n )

Generate a formula with n quadrature points.

Definition at line 1262 of file quadrature_lib.cc.

## ◆ QGaussChebyshev() [2/2]

 QGaussChebyshev< 1 >::QGaussChebyshev ( const unsigned int n )

Definition at line 1246 of file quadrature_lib.cc.

The documentation for this class was generated from the following files: