Reference documentation for deal.II version GIT relicensing-1291-gf3a46e514e 2024-07-24 11:20:02+00:00
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QGaussChebyshev< dim > Class Template Reference

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

Inheritance diagram for QGaussChebyshev< dim >:
Inheritance graph

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

◆ QGaussChebyshev() [2/2]

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

Definition at line 1246 of file

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