Hi folks,
I have a very simple question. I am playing around with the integrators, and attempt to reproduce the solutions of my ODEs by GSL ODE solvers... However there is substantial lack of match so far between the solutions that these latter give me with respect to the ones provided by Dopri/Radau integrators.
Could you point out please what exactly these integrators are in terms of numerical methods. The link on the online tutorial is broken at the moment (see here).
Thanks.
M
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
As the docs point out, both Dopri and Radau originate from Hairer and
Wanner. While I no longer have access to the wiki source to edit the
docs online, the FTP of the original code isn't even really necessary.
The code is all included in PyDSTool, since we compile it. You can
read more in their two-volume Springer books on integrating ODEs with
stiff and non-stiff methods. The citations and code are all here:
Depending on the problem, it can be very easy for different
integrators to diverge in their computed solutions. Sometimes, a lot
of work has to go into analyzing the situation to choose parameters
most appropriately to ensure accuracy, especially if over a long
integration time.
Hi folks,
I have a very simple question. I am playing around with the integrators, and
attempt to reproduce the solutions of my ODEs by GSL ODE solvers... However
there is substantial lack of match so far between the solutions that these
latter give me with respect to the ones provided by Dopri/Radau integrators.
Could you point out please what exactly these integrators are in terms of
numerical methods. The link on the online tutorial is broken at the moment
(see here).
Hi Rob,
thanks for the link!
I managed by it to recode the Dopri in C/C++ and solve one of my problems (this was few days after your post, but it took a while to reply as I have been relocating to Europe meanwhile...).
On a follow-up on this issue, could you please point me where to find in the PyDSTool code the routines to compute the Jacobian numerically? I need to use the Radau (after recoding it in C++), but I cannot provide an analytical form for the Jacobian of my system to the integrator (as it would become prohibitive to estimate). PyDSTool allows to integrate by Radau even if the Jacobian is not given, but Hairer's Radau routines require it instead. Accordingly, I believe that somewhere in PyDSTool, there is a routine for numerical estimation of the Jacobian, but I cannot find where this code is.
Thanks,
M
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
A follow up on this. Radau's comes already with a code snippet that allows numerical computation of the Jacobian, and this is set by opportune flag upon invocation. Forget my comment above.
If you would like to refer to this comment somewhere else in this project, copy and paste the following link:
Hi folks,
I have a very simple question. I am playing around with the integrators, and attempt to reproduce the solutions of my ODEs by GSL ODE solvers... However there is substantial lack of match so far between the solutions that these latter give me with respect to the ones provided by Dopri/Radau integrators.
Could you point out please what exactly these integrators are in terms of numerical methods. The link on the online tutorial is broken at the moment (see here).
Thanks.
M
As the docs point out, both Dopri and Radau originate from Hairer and
Wanner. While I no longer have access to the wiki source to edit the
docs online, the FTP of the original code isn't even really necessary.
The code is all included in PyDSTool, since we compile it. You can
read more in their two-volume Springer books on integrating ODEs with
stiff and non-stiff methods. The citations and code are all here:
http://www.unige.ch/~hairer/software.html
Depending on the problem, it can be very easy for different
integrators to diverge in their computed solutions. Sometimes, a lot
of work has to go into analyzing the situation to choose parameters
most appropriately to ensure accuracy, especially if over a long
integration time.
On Mon, Nov 28, 2016 at 4:37 PM, Maurizio De Pitta'
mauriziodepitta@users.sf.net wrote:
Hi Rob,
thanks for the link!
I managed by it to recode the Dopri in C/C++ and solve one of my problems (this was few days after your post, but it took a while to reply as I have been relocating to Europe meanwhile...).
On a follow-up on this issue, could you please point me where to find in the PyDSTool code the routines to compute the Jacobian numerically? I need to use the Radau (after recoding it in C++), but I cannot provide an analytical form for the Jacobian of my system to the integrator (as it would become prohibitive to estimate). PyDSTool allows to integrate by Radau even if the Jacobian is not given, but Hairer's Radau routines require it instead. Accordingly, I believe that somewhere in PyDSTool, there is a routine for numerical estimation of the Jacobian, but I cannot find where this code is.
Thanks,
M
A follow up on this. Radau's comes already with a code snippet that allows numerical computation of the Jacobian, and this is set by opportune flag upon invocation. Forget my comment above.