Chebyshev1GaussQuadrature

This routine computes the n Gauss-Quadrature points.

All Gauss-Quadrature points are inside $(-1, 1)$

Interface

܀ Interface

INTERFACE
  MODULE SUBROUTINE Chebyshev1GaussQuadrature(n, pt, wt)
    INTEGER(I4B), INTENT(IN) :: n
    !! It represents the order of Chebyshev1 polynomial
    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 Chebyshev1GaussQuadrature
END INTERFACE

️܀ See example

This example shows the usage of Chebyshev1GaussQuadrature method.

This routine returns the quadrature points for Chebyshev1 polynom.

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

  n = 3
  call reallocate(pt, n, wt, n)
  call Chebyshev1GaussQuadrature( n=n, pt=pt, wt=wt )
  msg = "Chebyshev1 Gauss Quadrature n = " // tostring( n )
  call display(msg%chars())
  astr = MdEncode( pt .COLCONCAT. wt )
  call display( astr%chars(), "" )
end program main

Results

pt	wt
-0.86603	1.0472
1.03412E-13	1.0472
0.86603	1.0472

↢

Chebyshev-Gauss Quadrature points

Chebyshev1 Gauss Quadrature n = 1

1.03412E-13	3.1416

Chebyshev1 Gauss Quadrature n = 2

-0.70711	1.5708
0.70711	1.5708

Chebyshev1 Gauss Quadrature n = 3

-0.86603	1.0472
1.03412E-13	1.0472
0.86603	1.0472

Chebyshev1 Gauss Quadrature n = 4

-0.92388	0.7854
-0.38268	0.7854
0.38268	0.7854
0.92388	0.7854

Chebyshev1 Gauss Quadrature n = 5

-0.95106	0.62832
-0.58779	0.62832
1.03412E-13	0.62832
0.58779	0.62832
0.95106	0.62832

Chebyshev1 Gauss Quadrature n = 6

-0.96593	0.5236
-0.70711	0.5236
-0.25882	0.5236
0.25882	0.5236
0.70711	0.5236
0.96593	0.5236

Chebyshev1 Gauss Quadrature n = 7

-0.97493	0.4488
-0.78183	0.4488
-0.43388	0.4488
1.03412E-13	0.4488
0.43388	0.4488
0.78183	0.4488
0.97493	0.4488

Chebyshev1 Gauss Quadrature n = 8

-0.98079	0.3927
-0.83147	0.3927
-0.55557	0.3927
-0.19509	0.3927
0.19509	0.3927
0.55557	0.3927
0.83147	0.3927
0.98079	0.3927

Chebyshev1 Gauss Quadrature n = 9

-0.98481	0.34907
-0.86603	0.34907
-0.64279	0.34907
-0.34202	0.34907
1.03412E-13	0.34907
0.34202	0.34907
0.64279	0.34907
0.86603	0.34907
0.98481	0.34907

Chebyshev1 Gauss Quadrature n = 10

-0.98769	0.31416
-0.89101	0.31416
-0.70711	0.31416
-0.45399	0.31416
-0.15643	0.31416
0.15643	0.31416
0.45399	0.31416
0.70711	0.31416
0.89101	0.31416
0.98769	0.31416