f22bf242-15b2-468b-9dd6-1955b1df7b5c 31 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

x f x 0.5 1 -^x - exp * :

a 109 -^: b 0.1 : c 0.25 : 13 mat

a f 31622.7766

restart MaximaControl Restart complete.

romberg load Maxima C:/maxima-5.40.0/bin/../share/maxima/5.40.0/share/numeric/romberg.lisp

rombergabs rombergit rombergmin rombergtol 41 sys Maxima 0110 0.0001 41 sys

http://maxima.sourceforge.net/docs/manual/de/maxima_67.html

rombergtol 0.01 MaximaDefine 0.01

rombergit 20 MaximaDefine 20

t.0 1 time :

x f x a b romberg Maxima 0.6133

t.1 1 time :

t.1 t.0 - 2.091 s *

rombergit 30 MaximaDefine 30

rombergtol 0.005 MaximaDefine 0.005

x f x a b romberg Maxima 0.6125

t.2 1 time :

t.2 t.1 - 3.931 s *

# MaximaLog Received Bytes: 34
(%i31) romberg(x^(0.5-1)*exp(-x),x,1/1000000000,1/10);
(%o31) 0.6125304748539697

Note that currently Maxima() has a built-in timeout of 5 seconds. If the calculation takes longer, the session is restarted. Probably, there should be an option to override this with a custom timeout.

Question/Answer:

1. The question is whether the iterative Simpson converges truly ?

2. For this example => Answer is YES. An infinitesimal analysis

will reveal that the smaller 'dx' => closer it tends to true value ...

for this particular example, as demonstrated. For other applications

one may check 1rst the convergence via Simpson(f,a,b,n).

]]>

x 0.1 :

sanity vs Mathematica π sqrt x sqrt erf * 0.611991

http://www.wolframalpha.com/input/?i=integrate+x%5E(0.5-1)*exp(-x)+from+0+to+0.1