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Offline Jean Giraud  
#1 Posted : 08 August 2017 15:22:30(UTC)
Jean Giraud


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As delivered, the Smath integrator accuracy is limited to "n subspace 10000".
The attached document exposes two examples that the native integrator fails.
It suggests to code for "n at least 1 000 000".
On your fast PC, will takes ~ 35 min to calculate the document.
Accordingly to Wolfram [Mathematica], they will fail no integration.
In Engineering works, this is not an option.
Conclusively: would be nice Smath implements the equivalent Mathcad/Mathsoft.
various integration options ... I don't have those codes [Mathsoft proprietary].

Jean

Integrate Adaptive Simpson.sm (31kb) downloaded 9 time(s).
Offline mkraska  
#2 Posted : 08 August 2017 17:10:58(UTC)
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2017-08-08 15_50_56-SMath Studio 0.98.6398 - [Romberg.sm_].png
Romberg.sm (14kb) downloaded 8 time(s).
Martin Kraska

Portable SMath with plugins and interactive handbook: http://smath.info/wiki/SMath%20with%20Plugins.ashx
Offline Jean Giraud  
#3 Posted : 09 August 2017 20:58:31(UTC)
Jean Giraud


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Hello Martin,

The Romberg integration transform improves significantly the accuracy
of the result when applicable. Mathcad 11 and earlier performs two tests
to validate application: a trapezoidal on some length and a Richardson
interpolation. If the two tests coincide on some pre-decided basis,
then Romberg is accepted. Otherwise, it performs a "Romberg open end"
[I don't know what it means], to decide an adaptive method [for which
I lost the code also].
From what you are saying, Maxima works on timing => looks weird, isn't it.
The attached exemplifies applicability. All that is because Simpson is
universally a good integrator, but NOT for all integrands.

Integrate Romberg Demo.sm (53kb) downloaded 6 time(s).
Offline mkraska  
#4 Posted : 10 August 2017 00:10:55(UTC)
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Timeout-problem resolved. http://smath.info/bts/Is.../IssueDetail.aspx?id=189


I am open to proposals on what integrator to use. The Maxima plugin has the option to search for a symbolic solution if symbolic optimization is requested. If numeric optimization is requested and no unresolved constants remain (units are ok) in the expression, then we could use whatever numeric procedure, be it from Maxima or whatever library.

Martin Kraska

Portable SMath with plugins and interactive handbook: http://smath.info/wiki/SMath%20with%20Plugins.ashx
Offline Jean Giraud  
#5 Posted : 10 August 2017 15:37:46(UTC)
Jean Giraud


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Originally Posted by: mkraska Go to Quoted Post
I am open to proposals on what integrator to use. The Maxima plugin has the option to search for a symbolic solution if symbolic optimization is requested. If numeric optimization is requested and no unresolved constants remain (units are ok) in the expression, then we could use whatever numeric procedure, be it from Maxima or whatever library.


The best library is the Mathcad/Mathsoft, don't know about Mathcad/PTC.
From all that I posted, easy to manage 'singular & infinite limit(s)'.
For those cases that need be checked for convergence [up to 1 000 000],
it is just a matter of increasing the "Integral accuracy" in options.

WolframAlpha is the piece of gold as it gives the indefinite integral
on top of the definite integral result [cumulative within limits].

Cheers, Jean

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