ADAPTIVE
QUADRATURE ALGORITM
*
* To approximate I = integral ( ( f(x) dx ) ) from a to b to within
* a given tolerance TOL:
*
* INPUT: endpoints a, b; tolerance TOL; limit N to number of levels
*
* OUTPUT: approximation APP or message that N is exceeded.
DOUBLE INTEGAL
ALGORITHM
*
* To approximate I = double integral ( ( f(x,y) dy dx ) ) with limits
* of integration from a to b for x and from c(x) to d(x) for y:
*
* INPUT: endpoints a, b; positive integers m, n.
*
* OUTPUT: approximation J to I.
GAUSSIAN
DOUBLE INTEGRAL ALGORITHM
*
* To approximate I = double integration ( ( f(x, y) dy dx ) ) with limits
* of integration from a to b for x and from c(x) to d(x) for y:
*
* INPUT: endpoints a, b; positive integers m, n. (Assume that the
* roots r(i,j) and coefficients c(i,j) are available for
* i equals m and n for 1<= j <= i.
*
* OUTPUT: approximation J to I.
GAUSSIAN
TRIPLE INTEGRAL ALGORITHM
*
* To approximate I = triple integral ( ( f(x,y,z) dz dy dx ) ) with limits
* of integration from a to b for x, from c(x) to d(x) for y, and from
* alpha(x,y) to beta(x,y) for z.
*
* INPUT: endpoints a, b; postive integers m, n, p. (Assume that the
* roots r(i,j) and coefficients c(i,j) are available for i
* equals m, n, and p and for 1 <= j <= i.
*
* OUTPUT: approximation J TO I.
ROMBERG ALGORITHM
*
* To approximate I = integral ( ( f(x) dx ) ) from a to b:
*
* INPUT: endpoints a, b; integer n.
*
* OUTPUT: an array R. ( R(2,n) is the approximation to I. )
*
* R is computed by rows; only 2 rows saved in storage .
SIMPSON'S
COMPOSITE ALGORITHM
*
* To approximate I = integral ( ( f(x) dx ) ) from a to b:
*
* INPUT: endpoints a, b; even positive integer n.
*
* OUTPUT: approximation XI to I.