D101 Integration by Simpson's Rule

Function subprograms SIMPS and DSIMPS use Simpson's rule to compute an approximate value of the integral

$I\; =\; \int$_A^Bf(x)dx.

On CDC or Cray computers, the double-precision version DSIMPS is not available.

Structure:

FUNCTION subprograms
User Entry Names: SIMPS, DSIMPS
Files Referenced: Unit 6
External References: MTLMTR (N002), ABEND (Z035)

Usage:

In any arithmetic expression, SIMPS(F,A,B,N) or DSIMPS(F,A,B,N)

has the approximate value of the integral I, where SIMPS is of type REAL and DSIMPS is of type DOUBLE PRECISION, and F, A, B have the same type as the function name. N is of type INTEGER.

F

One-dimensional array with dimension (0:d), where $d\; \ge N$ , containing the value of $f(x)$ at $N+1$

equally-spaced points $x$_i, (i=0,1,...,N) , with $x$₀= A and $x$_N= B .

A,B

End-points of integration interval.

N

As defined above. N must be positive and even.

Error handling:

Error D101.1: $N\; \le 0$ or $N$ odd. The function value is set equal to zero, and a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.
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D102