UltrasphericalGaussQuadrature

This routine computes the n Gauss-Quadrature points.

Interface

܀ Interface
️܀ See example
↢

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

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

Interface​

Interface