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

Examples​

Examples