I think many users (including me) would like to start with academic examples, 
e.g. u_t=f(u)+g(u), when they try to learn PETSc TS solvers. This simple form 
allows for easy switch between all kinds of different integration methods.

Experienced users or experts who need to solve DAEs or complicate problems 
involving nontrivial mass matrix should be encouraged to try 
IFunction/IJacobian. Of course, we need better documentation to help them 
realize the switching is not always possible. Personally it took me a long time 
to get used to the IFunction business since I had been using u_t=f(u)+g(u) for 
a couple years before I jumped on PETSc. If we add support for this simple 
form, the learning curve would be less steep than it currently is.

Hong (Mr.)
 
> On Feb 14, 2017, at 11:55 AM, Jed Brown <[email protected]> wrote:
> 
> Barry Smith <[email protected]> writes:
>>  Hence my suggestion to have TSSetLeftHandSideFunction() (or Jed's 
>> suggestion to have multiple Right Hand side functions) this will allow 
>> comparison of implicit, explicit, imex without recompiling (which we don't 
>> have currently) for the case with no mass matrix. With a mass matrix, unless 
>> we use mass lumping and have a TSSetMassMatrix() you cannot switch to full 
>> explicit, but that is due to mathematics, not the interface.
> 
> Who in reality has a problem that looks like
> 
>  u_t = f(u) + g(u) + h(u)
> 
> where it may make sense to move some of this to the left (implicit)?
> I'm concerned that this isn't natural for many applications so adding an
> interface would be solving a problem that doesn't really exist outside
> perhaps a few academic examples.

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