UltrasphericalGaussQuadrature

This routine computes the n Gauss-Quadrature points.

Interface

܀ Interface

INTERFACE
  MODULE SUBROUTINE UltrasphericalGaussQuadrature(n, lambda, pt, wt)
    INTEGER(I4B), INTENT(IN) :: n
    !! It represents the order of Ultraspherical polynomial
    REAL(DFP), INTENT(IN) :: lambda
    !! lambda should be greater than -0.5
    REAL(DFP), INTENT(OUT) :: pt(:)
    !! the size is 1 to n
    REAL(DFP), OPTIONAL, INTENT(OUT) :: wt(:)
    !! the size is 1 to n
  END SUBROUTINE UltrasphericalGaussQuadrature
END INTERFACE

️܀ See example

This example shows the usage of UltrasphericalGaussQuadrature method.

This routine returns the quadrature points for Ultraspherical polynom.

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 = 1; call callme

See results

Ultraspherical Gauss Quadrature n = 1

pt	wt
0	2

  n = 2; call callme

See results

Ultraspherical Gauss Quadrature n = 2

pt	wt
-0.57735	1
0.57735	1

  n = 3; call callme

See results

Ultraspherical Gauss Quadrature n = 3

pt	wt
-0.7746	0.55556
-3.38271E-17	0.88889
0.7746	0.55556

  n = 4; call callme

See results

Ultraspherical Gauss Quadrature n = 4

pt	wt
-0.86114	0.34785
-0.33998	0.65215
0.33998	0.65215
0.86114	0.34785

  n = 5; call callme

See results

Ultraspherical Gauss Quadrature n = 5

pt	wt
-0.90618	0.23693
-0.53847	0.47863
-1.56541E-16	0.56889
0.53847	0.47863
0.90618	0.23693

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

end program main

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