Chebyshev1GaussRadauQuadrature

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

INTERFACE
  MODULE SUBROUTINE Chebyshev1GaussRadauQuadrature(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 Chebyshev1 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 Chebyshev1GaussRadauQuadrature
END INTERFACE

Examples

️܀ See example
↢

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 = 3; a=left; call callme
  n = 3; a=right; call callme
  contains
  subroutine callme
    call reallocate( pt, n+1, wt, n+1 )
    call Chebyshev1GaussRadauQuadrature( a=a, n=n, &
      & pt=pt, wt=wt )
    msg="Chebyshev1 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

Chebyshev1 Gauss Radau points, n+1 = 4


-1	0.2244
-0.62349	0.4488
0.22252	0.4488
0.90097	0.4488

Chebyshev1 Gauss Radau points, n+1 = 4


-0.90097	0.2244
-0.22252	0.4488
0.62349	0.4488
1	0.4488

Examples​

Examples