Chebyshev1GaussLobattoQuadrature

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

Interface

܀ Interface

INTERFACE
  MODULE SUBROUTINE Chebyshev1GaussLobattoQuadrature(n, pt, wt)
    INTEGER(I4B), INTENT(IN) :: n
    !! order of Chebyshev1 polynomials
    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 Chebyshev1GaussLobattoQuadrature
END INTERFACE

️܀ See example

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 ), allocatable :: pt( : ), wt( : )
  type(string) :: msg, astr
  n = 3
  call reallocate( pt, n+2, wt, n+2 )
  call Chebyshev1GaussLobattoQuadrature( n=n, &
    & pt=pt, wt=wt )
  msg="Chebyshev1 Gauss Lobatto points, n+2 = " &
      & // tostring( n+2 )
  call display(msg%chars())
  astr = MdEncode( pt .COLCONCAT. wt )
  call display( astr%chars(), "" )
end program main

Chebyshev1 Gauss Lobatto points, n+2 = 4

pt	wt
-1	0.3927
-0.70711	0.7854
1.03412E-13	0.7854
0.70711	0.7854
1	0.3927

↢

Some Chebyshev Gauss Lobatto Quadrature points

n+2 = 3

-1	0.7854
1.03412E-13	1.5708
1	0.7854

n+2 = 4

-1	0.5236
-0.5	1.0472
0.5	1.0472
1	0.5236

n+2 = 5

-1	0.3927
-0.70711	0.7854
1.03412E-13	0.7854
0.70711	0.7854
1	0.3927

n+2 = 6

-1	0.31416
-0.80902	0.62832
-0.30902	0.62832
0.30902	0.62832
0.80902	0.62832
1	0.31416

n+2 = 7

-1	0.2618
-0.86603	0.5236
-0.5	0.5236
1.03412E-13	0.5236
0.5	0.5236
0.86603	0.5236
1	0.2618

n+2 = 8

-1	0.2244
-0.90097	0.4488
-0.62349	0.4488
-0.22252	0.4488
0.22252	0.4488
0.62349	0.4488
0.90097	0.4488
1	0.2244

n+2 = 9

-1	0.19635
-0.92388	0.3927
-0.70711	0.3927
-0.38268	0.3927
1.03412E-13	0.3927
0.38268	0.3927
0.70711	0.3927
0.92388	0.3927
1	0.19635

n+2 = 10

-1	0.17453
-0.93969	0.34907
-0.76604	0.34907
-0.5	0.34907
-0.17365	0.34907
0.17365	0.34907
0.5	0.34907
0.76604	0.34907
0.93969	0.34907
1	0.17453