Reference documentation for deal.II version 9.6.1
 
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
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QGaussChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussChebyshev< dim >:

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.

Constructor & Destructor Documentation

◆ 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: