D106 Gaussian Quadrature with Five- and Six-Point Rules

Subroutine subprograms RGS56P and DGS56P calculate an approximation and uncertainty for the integral

$I\; =\; \int$_a^bf(x) dx

equal respectively to the mean value and the difference of the results $I$₅ and $I$₆ obtained by the five- and six-point Gaussian integration rules.

On CDC and Cray computers, the double-precision version DGS56P is not available.

Structure:

SUBROUTINE subprograms
User Entry Names: RGS56P, DGS56P
External References: User-supplied FUNCTION subprogram.

Usage:

For $t=R$ (type REAL), $t=D$ (type DOUBLE PRECISION),

    CALL tGS56P(F,A,B,RES,ERR)

F

(type according to t) Name of a user-supplied FUNCTION subprogram, declared EXTERNAL in the calling program. This subprogram must set $F(X)=\; f(X)$ .

A,B

(type according to t) End-points of integration interval. Note that B may be less than A.

RES

(type according to t) The calculated approximation for I, i.e. $\{12\}(I$₅+I₆) ,

ERR

(type according to t) An estimated uncertainty on this approximation, i.e. $|I$₅-I₆| .

D107