Hello All,

I'm solving a multiple component non-linear reaction-diffusion problem with 
dealii and for time stepping I'm using the embedded explicit methods 
available within the dealii framework. 

If I understand the documentation correctly, the embedded method should 
coarsen the time step if the error is less than the parameter 'coarsen_tol 
<https://dealii.org/8.4.1/doxygen/deal.II/classTimeStepping_1_1EmbeddedExplicitRungeKutta.html#aca772056c3e45631020ba0b3175ac2cf>'.
 
This, however, does not seem to work! The error norm obtained by calling 
get_status().error_norm on the embedded explicit runge kutta method returns 
a value in the order of 1e-23(or even 0 for some methods) at all time 
steps, while my coarsen tolerance is set to  1e-10. The time step for the 
next iteration is still not coarsened, it always uses the initial time step 
I supply. 

The way I implement the time stepping is exactly the same as the way it is 
implemented in step 52 tutorial program. I would also like to mention that 
the problem I'm solving is stiff and hence I'm using the embedded methods 
for their ability to adapt step size.

The questions I have are as follows:

1. What is wrong with the embedded method? Does the problem lie in my 
understanding?
2. Are embedded methods(with small time steps) a good choice for stiff 
problems or should I switch to an implicit method?


Regards,
Vaibhav

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