simple integrals give give difficult results - Сообщения
#1 Опубликовано: 12.08.2019 16:52:05
Integrating the simple functions 1/x, 1/x², 1/x³ upwards from 1 give correct results for low values of the upper limit but with the upper limit in the order of 200 or higher the results are not what I would expect. Please see the attached worksheet.
Is there a problem with the integral function or is there something I haven't grasped?
H
integral.sm
Is there a problem with the integral function or is there something I haven't grasped?
H
integral.sm
#2 Опубликовано: 13.08.2019 01:33:32
Hi. It's because the integral it's a numerical procedure, and maybe not a very robust one. So, like any numerical method, if it don't work, just use another.
integral.sm
Best regards.
Alvaro.
integral.sm
Best regards.
Alvaro.
#3 Опубликовано: 13.08.2019 05:04:21
Hakelm,
I opened your file and the results were correct. Therefore I believe that the parameter for the accuracy of the integrals in your SMath installation is not correctly set.
Try to change Tools->Options->Calculation->Integral Accuracy
For example, write 1000
However, Alvaro's considerations must be kept in mind
sergio
I opened your file and the results were correct. Therefore I believe that the parameter for the accuracy of the integrals in your SMath installation is not correctly set.
Try to change Tools->Options->Calculation->Integral Accuracy
For example, write 1000
However, Alvaro's considerations must be kept in mind
sergio
#4 Опубликовано: 13.08.2019 06:50:17
Many thanks for two very good answers!
Now I know that Smath doesn't know even the simplest of integrals but that approximation accuracy can be improved upon.
Even if I understand my system doesn't (SMathStudioDesktop.0_99_7109.Mono on Ubuntu 16.04).
It can't find the function Rkadapt.
I guess that the Runge-Kutta functions are to be found i some plugin. Where can I find that?
H
Now I know that Smath doesn't know even the simplest of integrals but that approximation accuracy can be improved upon.
Even if I understand my system doesn't (SMathStudioDesktop.0_99_7109.Mono on Ubuntu 16.04).
It can't find the function Rkadapt.
I guess that the Runge-Kutta functions are to be found i some plugin. Where can I find that?
H
#5 Опубликовано: 13.08.2019 08:44:46
I guess that the Runge-Kutta functions are to be found i some plugin. Where can I find that?
ODE Solvers.
Russia ☭ forever, Viacheslav N. Mezentsev
#6 Опубликовано: 13.08.2019 10:35:06
Is there a problem with the integral function or is there something I haven't grasped?
The Simpson integrator ranges from exact to freak.
In your examples, increase the integral accuracy from
menu, options, calculations, integral accuracy [max 10000]
Wise to sanity Wolfram Alpha cost is 0.00 $
integral.sm
#7 Опубликовано: 14.08.2019 10:19:49
May I assume that the SMath-integral is made using Simpson's rule and that the integral accuracy [max 10000] is the number of steps taken by Simpson?
H
H
#8 Опубликовано: 14.08.2019 11:14:29
May I assume that the SMath-integral is made using Simpson's rule and that the integral accuracy [max 10000] is the number of steps taken by Simpson?
Quite right: The Smath integrator is Simpson.
Ranged accuracy [50 ... 10000]. Trivial cases are exact.
Two more exact cases are know 1/x [ln(x), b_spline].
On long range of the variate 'x' the Simpson/Romberg kernel
gives a much better result than simple Simpson.
Carlos adaptive algorithm is fool proof all cases.
You want these two proposed ... reply YES/NO.
Jean
#9 Опубликовано: 14.08.2019 13:53:22
Yes please
H
H
#10 Опубликовано: 14.08.2019 19:07:51
As you can see, Romberg has the virtue of reducing the range of integration
in the [0 ... 1 ] domain. In two versions directly associated with the
Smath native Simpson integrator or Simpson algo style, thus integration
accuracy 'n' @ the user command line.
These two documents are like minimalist tool box.
Jean
Integrate Compendium_1 Romberg_FD_Adaptive [Carlos].sm
Integrate Compendium_21 Simpson-Romberg Merit.sm
in the [0 ... 1 ] domain. In two versions directly associated with the
Smath native Simpson integrator or Simpson algo style, thus integration
accuracy 'n' @ the user command line.
These two documents are like minimalist tool box.
Jean
Integrate Compendium_1 Romberg_FD_Adaptive [Carlos].sm
Integrate Compendium_21 Simpson-Romberg Merit.sm
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