HP HP-20S - Numerical Integration (int)

Error - LbL is displayed if the iteration count is exceeded. This means
that for the initial guess provided, the program cannot converge on a
root within count iterations. Try a new guess that is closer to the root,
examine the function to see if it has no real roots, or increase the
iteration count, ¢, or Ax limit. (Refer to program instruction steps 6
through 8.)
If an error occurs, check the root approximation (in Rg) to see if it is
close enough.
If the function being solved has multiple roots, you can use this pro-
gram to find each root by selecting different initial guesses that are
close to each of the different roots.
The value of f(x) for any x can be calculated by entering the value for
x and pressing F.
If there is a pending expression when the initial guess (x) is entered,
it is ignored.
The program uses the equations:
Newton’s
Method:
X=X
—
fex)
f(x;)
Derivative
Approximation:
filx,)
=
w
5.
1
where 6, = x; _; — x;, 69 = 10°x, if x; # 0 and 6, = 107 if x, = 0.
Convergence Criteria: M\ < Axlimitor |x; . ; — x| =0,
Xi
and |x;| # 0 and |f(x)| < ¢ within count
iterations
Numerical Integration (int)
This program calculates an approximate integral for f(x) using
Simpson’s rule. You must define the function f(x) by entering the pro-
gram lines that are required to calculate f(x), assuming x is in the
display. You must also supply the number of intervals, n, for the inte-
gral. The larger the number of intervals, the more accurate the answer
is, but the more slowly the program will calculate an answer.
7: Built-in Program Library 91