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Offline Jean Giraud  
#1 Posted : 03 April 2019 06:57:48(UTC)
Jean Giraud


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Publications confuse themselves: this not Finite Differences.
Finite Differences [FD] concern Data Sets.

Jean

Derivative Infinitesimal Analysis.sm (48kb) downloaded 37 time(s).
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Offline omorr  
#2 Posted : 04 April 2019 09:37:17(UTC)
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I have to say that I am just sad that something like this is not easily performed in SMath

difint.PNG

Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
Offline Jean Giraud  
#3 Posted : 04 April 2019 16:25:07(UTC)
Jean Giraud


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Originally Posted by: omorr Go to Quoted Post
I have to say that I am just sad that something like this is not easily performed in SMath

In your demo, a small epsilon was added to avoid singular matrix.
Interesting: Mathcad copes naturally.
we have same as Mathcad:
1. the spline system [l_p_cspline] at choice
2. first derivative
3. vectorized cumulative
4. additional 2nd derivative ...
On that one, check what you get from Mathcad.
This document can be refactored more professional for extensive use.

Jean

Radovan.sm (85kb) downloaded 18 time(s).

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Online Razonar  
#4 Posted : 05 April 2019 02:50:41(UTC)
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Originally Posted by: omorr Go to Quoted Post
I have to say that I am just sad that something like this is not easily performed in SMath

Regards,
Radovan


Yes, it is. For this, and for the issues in the extreme of the interpolation intervals and the importance of that in solve differential equations I write this:

Originally Posted by: Razonar Go to Quoted Post
Derivative and integral for regular cubic splines.
Best regards.
Alvaro.

di cspline test.sm (87kb) downloaded 33 time(s).


Best regards.
Alvaro.

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Offline Jean Giraud  
#5 Posted : 05 April 2019 06:31:29(UTC)
Jean Giraud


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Originally Posted by: Razonar Go to Quoted Post
Yes, it is. For this, and for the issues in the extreme of the interpolation intervals and the importance of that in solve differential equations

On that point, Mathcad ODEsolve is based on 'lspline'.
Remember it was explored in the Mathsoft Collaboratory.
Thanks, most profitable, just finished converting the code
to normal variable names ...
in the last CS.V(X,Y) ... 'c' created red, thus replaced by 'q'.

At the time I checked those splines, Mathcad code is same as Matlab.
Matlab tutorial was about 10 pages long ending to same Mathcad tridiagonal.
Sanity was checked Mathematica 4.0. Those basic codes were borrowed
from the big ACM library. All same as Smath cinterp.

Jean
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Online Razonar  
#6 Posted : 05 April 2019 08:56:39(UTC)
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Originally Posted by: omorr Go to Quoted Post
I have to say that I am just sad that something like this is not easily performed in SMath
Radovan


Some notes about Radovan's sadness :-(

CinterpQuickDiffInt.sm (31kb) downloaded 25 time(s).

Best regards.
Alvaro

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Offline Jean Giraud  
#7 Posted : 05 April 2019 19:48:01(UTC)
Jean Giraud


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Originally Posted by: Razonar Go to Quoted Post
Some notes about Radovan's sadness

True: Smath "cinterp" is not the best companion and not recognized
vs other CAS. As demonstrated in the attached, not as accurate.

Jean

Spline0 l_p_cspline Dspline,Cumul Copy.sm (84kb) downloaded 18 time(s).
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