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

Jean

Derivative Infinitesimal Analysis.sm (47,75 KiB) scaricato 1331 volta(e).

I have to say that I am just sad that something like this is not easily performed in SMath



Regards,
Radovan

Wrote

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 (84,44 KiB) scaricato 1278 volta(e).

Wrote

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:

Wrote

Derivative and integral for regular cubic splines.
Best regards.
Alvaro.

di cspline test.sm (86,48 KiB) scaricato 1538 volta(e).

Best regards.
Alvaro.

Wrote

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

Wrote

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 (30,17 KiB) scaricato 1333 volta(e).

Best regards.
Alvaro

Wrote

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 (83,66 KiB) scaricato 1334 volta(e).