grid_Inv_Cheb

function grid_Inv_Cheb(x, left, right, n)

Description:

Inverts the formula

for Chebychev gridpoints on the interval , such that

If is equal to a particular gridpoint created by the subroutine grid_Cons_Cheb, then the return value of this function is the integer index . If lies in between two gridpoints values, the function will return a value in between the two integer indices of the gridpoints according to the above formula.

Input arguments:

• real*8 :: x    or    real*8 :: x(:)
  The gridpoint of which to calculate the index, corresponds to . This can be either a scalar or a one-dimensional array containing many different gridpoints.
• real*8 :: left
  The left interval endpoint, corresponds to .
• real*8 :: right
  The right interval endpoint, corresponds to .
• integer :: n
  The number of gridpoints to use, corresponds to .

Return Value:

• real*8 :: grid_Inv_Cheb    or    real*8 :: grid_Inv_Cheb(:)
  The index of the Chebychev gridpoint i. This is a scalar if x is a scalar and a one-dimensional array if x is an array.

References

• For further reading refer to:
  • Süli, E. & Mayers, D. F. (2003). An Introduction to Numerical Analysis. Cambridge: Cambridge University Press.
  • Powell, M.J.D. (1996). Approximation Theory and Methods. Cambridge: Cambridge University Press.