LegendreGaussRadauQuadrature

This routine returns the $n+1$ Quadrature points and weights.

INTERFACE
  MODULE SUBROUTINE LegendreGaussRadauQuadrature(a, n, pt, wt)
    REAL(DFP), INTENT(IN) :: a
    !! the value of one of the end points
    !! it should be either -1 or +1
    INTEGER(I4B), INTENT(IN) :: n
    !! order of Legendre polynomial
    REAL(DFP), INTENT(OUT) :: pt(:)
    !! n+1 quadrature points from 1 to n+1
    REAL(DFP), OPTIONAL, INTENT(OUT) :: wt(:)
    !! n+1 weights from 1 to n+1
  END SUBROUTINE LegendreGaussRadauQuadrature
END INTERFACE

a

• For left Radau points $a=-1$
• For right Radau points $a=1$

n

order Legendre polynomial, this rule has order of accuracy $2n$. It will return $n+1$ points.

pt and wt

Points and weights.

Examples

️܀ See example

This example shows the usage of LegendreGaussRadauQuadrature method.

This routine returns the quadrature points for Legendre polynomials.

Note that this routine returns n+1 quadrature points and one of the points will be end point.

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real( dfp ), allocatable :: pt( : ), wt( : )
  real( dfp ), parameter :: left=-1.0, right=1.0
  type(string) :: msg, astr
  real( dfp ) :: a
  n = 2; a=left; call callme
  n = 2; a=right; call callme
  contains
  subroutine callme
    call reallocate( pt, n+1, wt, n+1 )
    call LegendreGaussRadauQuadrature( a=a, n=n, &
      & pt=pt, wt=wt )
    msg="Legendre Gauss Radau points, n+1 = " &
        & // tostring( n+1 )
    call display(msg%chars())
    astr = MdEncode( pt .COLCONCAT. wt )
    call display( astr%chars(), "" )
  end subroutine callme
end program main

Legendre Gauss Radau points, n+1 = 3

pt	wt
-1	0.22222
-0.2899	1.025
0.6899	0.75281

Legendre Gauss Radau points, n+1 = 3

pt	wt
-0.6899	0.75281
0.2899	1.025
1	0.22222

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