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Reference documentation for deal.II version 9.6.0
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#include <deal.II/base/quadrature_lib.h>
Public Member Functions | |
QGaussChebyshev (const unsigned int n) | |
Generate a formula with n quadrature points. | |
QGaussChebyshev (const unsigned int n) | |
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< dim >::QGaussChebyshev | ( | const unsigned int | n | ) |
Generate a formula with n
quadrature points.
Definition at line 1262 of file quadrature_lib.cc.
QGaussChebyshev< 1 >::QGaussChebyshev | ( | const unsigned int | n | ) |
Definition at line 1246 of file quadrature_lib.cc.