Acron RPN announces v3.0 BETA
01-08-2018, 12:48 AM
Post: #33
 vanLudwig Member Posts: 50 Joined: Jun 2016
RE: Acron RPN announces v3.0 BETA
New functionality for integrals:

I continue to get all fifteen decimal places correct for my old test cases:
(I'm formatting $$\int_{a}^{b}f(x)dx$$ as $$\int \left (f(x), x, a, b \right )$$, since that's the way Acron RPN draws it.)
$\int \left ( x^{2}, x, 0, 1 \right )=0.333333333333333$
$\int \left ( \frac{1}{x}, x, 1, 10 \right )=2.30258509299405$

It now can tolerate open intervals, but accuracy suffers (correct up to the red digits)
$\int \left ( \frac{1}{\sqrt{x}}, x, 0, 1 \right )=1.9999{\color{Red} 869261464}$
$\int \left ( \frac{1}{\sqrt[3]{x}}, x, -1, 1 \right )=2.24999{\color{Red} 851776435}+1.29903{\color{Red} 724990752}i$

Integration over complex bounds
$\int \left ( \frac{\cos (x)}{x^{3}}, x, -1, i \right )=0.958325065720024+0.78539816339744{\color{Red} 9}i$

Double integrals
$\iint \left (\left (xe^{-x-2y}, x, 0, \infty \right ), y, 0, \infty \right )=0.500000{\color{Red} 133547982}$

And double integrals where the inner bounds are a function of the outer variable
$\iint \left (\left (\frac{e^{-y}}{y}, y, x, \infty \right ), x, 0, \infty \right )=1.00000{\color{Red} 986129641}$

The only thing I'm not happy with is that it frequently doesn't recognize divergent integrals, and gives somewhat reasonable looking answers.
$\int \left (\tan (x), x, 0, \frac{\pi }{2} \right )={\color{Red} 1002.00994626946}$

I'm using an adaptive Newton-Cotes quadrature based on Simpson for closed intervals and Milne for open intervals. I spin off two new threads for each successive iteration, and prioritize them by the error for that segment, so it is constantly attacking the worst problem and refining its answer until it either gets fifteen digits of precision, or runs out of time. That means faster devices will get more accurate answers, but everyone will get an answer in a reasonable amount of time.
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 Messages In This Thread Acron RPN announces v3.0 BETA - vanLudwig - 08-27-2017, 05:49 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 08-27-2017, 09:20 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 08-30-2017, 12:16 AM RE: Acron RPN announces v3.0 BETA - Nigel (UK) - 08-30-2017, 11:20 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 08-31-2017, 01:09 PM RE: Acron RPN announces v3.0 BETA - Nigel (UK) - 08-31-2017, 08:02 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 08-31-2017, 11:46 PM RE: Acron RPN announces v3.0 BETA - inaqui76 - 09-01-2017, 02:36 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-01-2017, 02:51 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-01-2017, 09:38 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-04-2017, 06:29 PM RE: Acron RPN announces v3.0 BETA - Nigel (UK) - 09-05-2017, 08:03 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-05-2017, 11:18 PM RE: Acron RPN announces v3.0 BETA - Nigel (UK) - 09-06-2017, 09:41 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-06-2017, 09:45 PM RE: Acron RPN announces v3.0 BETA - Dieter - 09-07-2017, 06:51 AM RE: Acron RPN announces v3.0 BETA - Dieter - 09-07-2017, 07:59 PM RE: Acron RPN announces v3.0 BETA - Nigel (UK) - 09-07-2017, 08:55 PM RE: Acron RPN announces v3.0 BETA - Paul Dale - 09-07-2017, 10:34 AM RE: Acron RPN announces v3.0 BETA - Dieter - 09-07-2017, 06:29 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-07-2017, 11:08 PM RE: Acron RPN announces v3.0 BETA - Paul Dale - 09-08-2017, 11:09 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-11-2017, 12:17 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 09-24-2017, 05:43 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 10-04-2017, 01:41 PM RE: Acron RPN announces v3.0 BETA - rprosperi - 10-05-2017, 12:37 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 10-05-2017, 02:44 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 10-05-2017, 12:54 PM RE: Acron RPN announces v3.0 BETA - rprosperi - 10-05-2017, 01:07 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 10-08-2017, 11:57 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 10-31-2017, 08:23 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 12-08-2017, 10:43 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 01-08-2018 12:48 AM RE: Acron RPN announces v3.0 BETA - sa-penguin - 01-15-2018, 01:40 AM RE: Acron RPN announces v3.0 BETA - Dieter - 06-15-2018, 06:26 PM RE: Acron RPN announces v3.0 BETA - The Shadow - 06-17-2018, 04:12 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 01-30-2018, 03:16 AM RE: Acron RPN announces v3.1.0 BETA - vanLudwig - 06-09-2018, 07:55 PM RE: Acron RPN announces v3.0 BETA - vanLudwig - 06-14-2018, 12:11 AM RE: Acron RPN announces v3.0 BETA - vanLudwig - 06-17-2018, 03:12 AM RE: Acron RPN announces v3.1.0 BETA - vanLudwig - 06-17-2018, 08:27 PM RE: Acron RPN announces v3.1.0 BETA - vanLudwig - 06-22-2018, 02:01 AM

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