Hello

Here is an example of integration using the Simpson recursive adaptive method.

Adaptive_Recursive_Simpson_SS6179.sm (13,29 KiB) scaricato 1342 volta(e).


On the other hand, when running the algorithm in the versions of Smath Studio 6179 and 7219,
I realize that the SS-6179 version is more accurate than the current SS-7219, since the
first one allows an error of 0.000000001, while the latter only allows an error of 0.000001



Adaptive_Recursive_Simpson_SS7219.sm (14,55 KiB) scaricato 1302 volta(e).

The SS-7219 version cannot calculate the function with an error of less than 0.000001 to achieve greater accuracy.

Are we going back?

Best Regards

Carlos

Wrote

On the other hand, when running the algorithm in the versions of Smath Studio 6179 and 7219,
I realize that the SS-6179 version is more accurate than the current SS-7219, since the
first one allows an error of 0.000000001, while the latter only allows an error of 0.000001

My native SS 6179 supports ε:=0.0000000000001
@ equivalent accuracy, Romberg-Simpson kernel runs ~ 8 times faster.
Most puzzling from version to version
On my slow laptop:
Romberg-Simpson ..... 12 s
Simpson recursive ... 96 s
Simpson kernel in Romberg range [0..1] at decimation [n]
is most valuable on large range of the integration variate 'x'.

Thanks Carlos, most interesting ... Jean.

Integrate Companion [Technical Accuracy Carlos Recursive].sm (29,14 KiB) scaricato 1143 volta(e).

Strange thing happened to my Win7 machine (SMath 7219) and both files (by Carlos and Jean).

Running both files will just close SMath without any warning.
See this animated gif please.



This does not happen to my Win10 machine.

Regards,
Radovan

On my machine win 7 (PRO 64bit) does not experience the problem of Radovan. Instead, I confirm the problem with the minimum precision value assigned

sergio

Wrote

Strange thing happened to my Win7 machine (SMath 7219) and both files (by Carlos and Jean).

What about separate each integrator and run 7219 ?
I guess you have tried. So, your Win 7 is kookoo.

Wrote

Wrote

Strange thing happened to my Win7 machine (SMath 7219) and both files (by Carlos and Jean).

What about separate each integrator and run 7219 ?
I guess you have tried. So, your Win 7 is kookoo.

Hello Jean,

Int() is going well but AdapRecursive() makes SMath to shut down when decreasing epsilon on my "kookoo" Win7

See this animated gif please.



Regards,
Radovan

Wrote

Int() is going well but AdapRecursive() makes SMath to shut down when decreasing epsilon on my "kookoo" Win7

Conclusion: Recursive code complains foo low epsilon.
But, that's what Carlos observed, isn't it ?
You may have to first define Recursive as a wild algo,
then insert parameters.

... download the MASTER Toolbox, updated a minute ago.
All my projects are based on those utilities.
Competitive with Mathcad/Mathsoft, Wolfram Alpha.
Here is ...

Integral 00000000 MASTER ToolBox Copy.sm (477,06 KiB) scaricato 1375 volta(e).