legendre - fabiankindermann/ce-fortran GitHub Wiki

subroutine legendre(x1, x2, x, w)

This subroutine calculates the nodes and weights for a Gauss-Legendre approximation of an integral

• real*8 :: x_1
  The left interval endpoint of the integration interval .
• real*8 :: x_2
  The right interval endpoint of the integration interval .

• real*8 :: x(:)
  A one-dimensional array into which the subroutine stores the nodes for the Gauss-Legendre approximation.
• real*8 :: w(:)
  A one-dimensional array into which the subroutine stores the weights for the Gauss-Legendre approximation. Note that w(:) needs to have exactly the same size as x(:).

• Parts of this routine were copied and adapted from:
  • Press, W.H., Teukolsky, S.A., Vetterling, W.T. & Flannery, B.P. (1992). Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing, 2nd edition. Cambridge: Cambridge Univeristy Press.
• For further reading refer to:
  • Stoer, J. & Bulirsch, R. (2002). Introduction to Numerical Analysis. New York: Springer Text in Applied Mathematics.
• This routine is used in the following programs:
  • prog02_13.f90