On 1/14/19 5:56 PM, D. Sarkar wrote:
>
> Thanks for the suggestions. Apologies for including the governing equation.
> The equation is shown below with a non-linear reaction term:
>
>
>
> I had looked at the example you suggested but will have to go over your video
> lectures.
> Using some assumptions, I was able to linearize the PDE and followed the
> transient heat equation example (step-26) by absorbing the linearized
> reaction
> term with the spatiotemporal source term.
Yes, that's the way to do it -- treat the diffusion term with an implicit time
discretization and make the reaction term explicit. You will have to choose a
small time step this way, but the advantage is that the equation then
essentially looks like the heat equation of step-26. If you want to choose
larger time steps, you can either be semi-implicit, for example using
a u^n / (b + u^{n-1})
for the reaction term, or make it fully implicit
a u^n / (b + u^n)
in which case you end up with a nonlinear system to solve in each time step --
which you would then do using something like step-15.
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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