UltrasphericalGaussLobattoQuadrature

This routine returns the $n+2$ Quadrature points and weights.

Interface

܀ Interface

INTERFACE
  MODULE SUBROUTINE UltrasphericalGaussLobattoQuadrature(n, lambda, pt, wt)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of Ultraspherical polynomials
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP), INTENT(OUT) :: pt(:)
    !! n+2 quad points indexed from 1 to n+2
    REAL(DFP), OPTIONAL, INTENT(OUT) :: wt(:)
    !! n+2 weights, index from 1 to n+2
  END SUBROUTINE UltrasphericalGaussLobattoQuadrature
END INTERFACE

️܀ See example

• This example shows the usage of UltrasphericalGaussLobattoQuadrature method.
• This routine returns the quadrature points for Ultraspherical weights.

Note that this routine returns n+2 points, the first point is -1 and last point is +1

program main
  use easifembase
  implicit none
  integer( i4b ) :: n
  real(dfp), parameter :: lambda=0.5_DFP
  real( dfp ), allocatable :: pt( : ), wt( : )
  type(string) :: msg, astr

  n = 0; call callme

See results

Ultraspherical Gauss Lobatto points, n+2 = 3

pt	wt
-1	0.33333
-4.48639E-17	1.3333
1	0.33333

  n = 1; call callme

See results

Ultraspherical Gauss Lobatto points, n+2 = 3

pt	wt
-1	0.33333
-4.48639E-17	1.3333
1	0.33333

  n = 2; call callme

See results

Ultraspherical Gauss Lobatto points, n+2 = 4

pt	wt
-1	0.16667
-0.44721	0.83333
0.44721	0.83333
1	0.16667

  n = 3; call callme

See results

Ultraspherical Gauss Lobatto points, n+2 = 4

pt	wt
-1	0.1
-0.65465	0.54444
-6.41178E-17	0.71111
0.65465	0.54444
1	0.1

  contains
    subroutine callme
    call reallocate( pt, n+2, wt, n+2 )
    call UltrasphericalGaussLobattoQuadrature( n=n, &
      & pt=pt, wt=wt, lambda=lambda )
    msg="Ultraspherical Gauss Lobatto points, n+2 = " &
        & // tostring( n+2 )
    call display(msg%chars())
    astr = MdEncode( pt .COLCONCAT. wt )
    call display( astr%chars(), "" )
  end subroutine callme

end program main

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