For TSBEULER (the theta method) see 
https://petsc.org/release/docs/manualpages/TS/TSTHETA.html 
<https://petsc.org/release/docs/manualpages/TS/TSTHETA.html> and look at the 
source code src/ts/impls/implicit/theta/teta.c for TSStep_Theta. You can use 
-snes_monitor_solution OPTIONS to see what the solutions are the nonlinear 
system look like as it solves the system.



  Barry



> On Oct 11, 2021, at 12:26 PM, Alfredo J Duarte Gomez <[email protected]> 
> wrote:
> 
> Good morning PETSC team,
> 
> I have  a working algorithm for my implicit TS integrator with a system of 
> ODE/DAE's, but I am observing a rather high number of iterations
> 
> I am currently using the simplest settings of a TSBEULER and setting a 
> constant time step.
> 
> My question  right now is whether the default settings use any sort of 
> initial guess algorithm before every time step. 
> 
> Since I have seen that the time step adapter calculates the Local Truncation 
> Error, it should be possible to use an extrapolation of arbitrary order of 
> accuracy as an initial guess for every time step right? Can someone indicate 
> how I would be able to use that?
> 
> Additionally, it would be very helpful to take a look at that initial guess, 
> is it possible to use any existing function to calculate it either in the 
> PreStep or PostStep function to visualize it?
> 
> Thank you,
> 
> -- 
> Alfredo Duarte
> Graduate Research Assistant
> The University of Texas at Austin

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