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<div><i>It seems like above you have already chosen a time
discretization, in that you have time steps appearing. The</i></div>
<i>
</i>
<div><i>idea with TS is to begin with the continuum form, in the
simplest case</i></div>
<div><i><br>
</i></div>
<div><i> u_t = G(u, t)</i></div>
<div><i><br>
</i></div>
<div><i>and in the implicit form</i></div>
<div><i><br>
</i></div>
<div><i> F(u_t, u, t) = 0</i></div>
<div>
<i><br>
</i></div>
<div><i>and let PETSc choose the time discretization (since there
are many multistep methods). It is likely that</i></div>
<div><i>you could reproduce the method you have above by choosing
one of the existing TS methods. Does this</i></div>
<i>
</i>
<div><i>make sense?</i></div>
<br>
<br>
Yes, I have tried that. I have perhaps not been clear with my
question. The discretization employed is simply Backward Euler. The
problem I see with trying to use TS is that my scheme uses u* as a
kind of predictor.<br>
<br>
I can write rewrite (u* - u_prev) + (tau )A u* = f1 as <br>
u*_t + A u* = f1; I apply backward Euler on this to find u* after
one time step.<br>
<br>
But the problem is the next part (u - u*) + (tau)B u = f2.<br>
This I can rewrite as u_t + B u = f2; But when I apply backward
euler, I want u_t = (u - u*)/tau.<br>
<br>
This breaks the pattern for use of the TS module, it seems to me. I
would like to know if I am correct in my assesment.<br>
Can I still use TS profitably, or do I need to implement my own
time stepper---that was my question.<br>
<br>
<br>
<br>
<br>
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