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LegendreQuadrature

This routine returns the Quadrature point of Legendre polynomial.

Interface​

INTERFACE
  MODULE SUBROUTINE LegendreQuadrature(n, pt, wt, quadType, onlyInside)
    INTEGER(I4B), INTENT(IN) :: n
    !! number of quadrature points, the order will be computed as follows
    !! for quadType = Gauss, n is same as order of Legendre polynomial
    !! for quadType = GaussRadauLeft or GaussRadauRight n is order+1
    !! for quadType = GaussLobatto, n = order+2
    REAL(DFP), INTENT(OUT) :: pt(n)
    !! n+1 quadrature points from 1 to n+1
    REAL(DFP), OPTIONAL, INTENT(OUT) :: wt(n)
    !! n+1 weights from 1 to n+1
    INTEGER(I4B), INTENT(IN) :: quadType
    !! Gauss
    !! GaussRadauLeft
    !! GaussRadauRight
    !! GaussLobatto
    LOGICAL(LGT), OPTIONAL, INTENT(IN) :: onlyInside
    !! only inside
  END SUBROUTINE LegendreQuadrature
END INTERFACE
n

n is the total number of quadrature points.

  • n point Gauss quadrature rule has 2n−12n-1 degree of accuracy.
  • n point Gauss-Radau quadrature rule has 2n−22n-2 degree of accuracy.
  • n point Gauss-Lobatto quadrature rule has 2n−32n-3 degree of accuracy.
quadType

Type of quadrature, following values are accepted:

  • Gauss
  • GaussRadauLeft
  • GaussRadauRight
  • GaussLobatto