After much tinkering, kudos to maple for the effectiveness of its sum command. As promised here is an improvement to mrb().

Here, mrb 2 is at least 20% more accuarte than mrb and mrb1.

 restart:

mrb2:=proc(e)
local a,b,c,d,s,k,n,m,w,x:

if e < 100 then n:=31+e;Digits:=31+e else
n:=131*round(e/100);Digits:=131*round(e/100) end if:
a:=array(0..n-1):
a[0]:=1:
for m from 1 to n-1 do
a[m]:=(m+1)^(1/(m+1)) od:
d:=(3+sqrt(8))^n:
d:=(d+1/d)/2:
b:=-1:
c:=-d:
s:=0:
for k from 0 to n-1 do c:=b-c:
b:=(k+n)*(k-n)*b/((k+1/2)*(k+1)):
s:=s+c*a[k] od:
w:=x->(x^(1/x)-1);
r:=1/2-s/d:result:=evalf(r+1/4*(w(10^(n+1))-w(10^(n+2))),e)
end proc;

Warning, `result` is implicitly declared local to procedure `mrb2`

 

 

> for a from 2 to 20 do mrb2(a) od;:

[same results as are found in, Improvements to MRB process part 1]

 mrb2(1000);
print(`output redirected...`); # input placeholder
0.187859642462067120248517934054273230055903094900138786172004684089477231564\

  660213703296654433107496903842345856258019061231370094759226630438929348896\

  184120837336626081613602738126379373435283212552763962171489321702076282062\

  171516715408412680448363541671998519768025275989389939144579835055613509648\

  521071207844423095868129497688526949564204255586483670441042527952471060666\

  092633974834103115781678641668915460034222258838002545539689294711421221891\

  050983287122773080200364452153905363950553322034706275511598128280395102192\

  649146731762935161906598160186642458249506972033819929584209355151625143993\

  576007645932912814517090824249158832041690664093344359148067055646928067870\

  070281150093806069381393859533606579874055620623487043293607378195646031047\

  639506648930613606455280675151935082808373767192968663981030949496374962773\

  830498463245634793115753002892125232918161956269736970748657654760711780171\

  957873683009659022606687536563055165673612881502014387561366865522106743053\

  7059103973575619148909458

m+(11^(2/3)-3^(1/2)-22)/100~=8.88E-8 For the numerically curious, there are many approximations involving the NRB Constant at QA-1.doc marvinrayburns.com
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Marvin Ray Burns

John, what is the difference between multi-dim integration and double, triple and multiple Integration? marvinrayburns.com
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Marvin Ray Burns

Concerning your first question: >>can maple 10 help me in building such simulators and plot there 3D plots of fluid motion in the medium? Have you searched the application center? You can enter your request in the above search engine and click the Maplesoft radio button. Even if you can't find exactly what you are asking for, some of the applications might be similar. Perhaps you could write one of those authors to help write an application that meets your needs. marvinrayburns.com
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Marvin Ray Burns

I must confess, I think of the web as a place for people to make themselves and ideas known, If others aren’t posting a lot, I don’t feel bad about using a little of their share of limelight.

I feel somewhat justified in answering questions and posting my (possibly meager) findings followed by a signature that gets me some attention.

I might be alone in that feeling; that’s fine. I just have a need for attention. Right now I seem offensive some people; only for the offence am I sorry. One great thing about the web, it is self-policing.

These posts still are not all I want them to be; I do try to do my tweaking in groups. That is better that tweaking one every hour.

I’ll try to leave these posts alone for a few days. Maybe I’ll get a new post written.

 

I believe that some of you could build upon the ideas I've only broached upon in this blog; I have written these comments for that purpose. Do not think I will be offended by your comments and constructive criticism. marvinrayburns.com
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Marvin Ray Burns

I'm almost convinced to buy maple 11; however, just a few concerns or desires. When the 64 bit version of Maple 11 becomes available for Vista Ultimate, will the maximum precision and maximum integer size be increased from what they are in maple 10 on XP, and by how much? Examples: when I was ruining maple 10 on XP with a 3GH PD with 3.25GB of RAM, even with the Command Line Interface, with integers like, 2^32582657-1 I got an un-operable “...Integer too large for display... . With the command evalf(sum((-1)^n*n^(1/n),n=1..infinity),5000);, I got a message indicating that there was insufficient memory. On the Command Line Interface, entering evalf(log(2),1000000); caused the interface to close down. Perhaps, I’m hoping for too much. Nonetheless, can you give me any stats concerning the maximum precision and maximum integer size of Maple 11 for Vista Ultimate with, say, 16GB RAM? Or should I expect them to remain about the same as maple 10 on XP? marvinrayburns.com
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Marvin Ray Burns

Since you can find your code in the text file, copy it. You might have to do it line by line, depending on how it's placed. Paste the lines into a new worksheet or document and it might not hurt to save it with a different name. marvinrayburns.com
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Marvin Ray Burns

I’ve wanted to zip through Blogs and Forums faster and the recent post does do what I want. However, I only now took note of it. Recent Blog and Recent Forum buttons next to Blogs and Forums would be more conspicuous. marvinrayburns.com
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Marvin Ray Burns My Desire

Arthur75, To show the less than sign in your code, you can use the charactors: & l t ; with no spces between them. Like: < My Desire

banengineer, They asked everything that I was thinking. One more thing: You could back-up everything you want to save, if possible including updates, but not Maple; restore your computer and then reinstall Maple. If Maple won't then install then it is indeed at fault. Marvin My Desire