[sundials-users] How to choose suitable values of relative and absolute tolerances

[utpal kiran]

Hi, 

What are the typical values of relative and absolute tolerances used for solving large ODE systems? 

I am able to solve a stiff problem having 53 equations with reltol = 1e-6 and abstol = 1e-11.  Currently, I am trying to solve even bigger problems having no. of equations up to 1034. However, I am getting convergence related issues that lead to further reduction of tolerance values. I also saw on several forum posts that typical values of the tolerance is around 1E-10. Therefore, I would like to know about values of tolerances that are sufficient to solve large stiff problems. How do tolerances vary with the size of ODE systems? Is there any lower limit on the value of absolute tolerance ?

Thank you,

Utpal Kiran

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[Woodward, Carol S.]

Hi Utpal Kiran,

 

Tolerances are generally application dependent as they reflect the amount of accuracy you want to derive from each time step.  The integrators in SUNDIALS will use these to govern the size of steps, and for CVODE and iDA also the order of method.  I suggest taking a look at the FAQ article on choosing tolerances and consider what makes sense for your problem specifically.  This has a nice explanation of the differences between absolute and relative tolerances.

 

https://computing.llnl.gov/projects/sundials/faq#cvode_tols

 

--Carol