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Solve two species coupled linear reaction-functional diffusion

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Isaac
Isaac 2013-5-5
Hi everyone,
I am looking to solve some coupled pdes with neumann zero-flux bc and random ic. Ideally I would like to have a 2d or 3d solution but 1d will suffice for now. The two species involve a functional diffusion model which considers the difference in diffusion between the two species. This difference is then considered by a sigmoidal function to define positive or negative flow. There is also exponential decay of each of the species.
du/dt = - a1*u + 1/(1+exp(a2*d2u/dx2-a3*d2v/dx2)) - 1/2
dv/dt = - a4*v + 1/(1+exp(a5*d2u/dx2-a6*d2v/dx2)) - 1/2
Does anyone know of any off the shelf tools in matlab that can do this? I have the code running in mathematica but it is painfully slow.
Thanks for your help in advance :)

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回答（1 个）

Zhang lu
Zhang lu 2013-5-5
编辑：Zhang lu 2013-5-5
you can convert the pde function as follow
d2u/dx2=[a5*ln(1/(du/dt+a1*u+1/2)-1)-a2*ln(1/(dv/dt+a1*u+1/2)-1)]/(a2*a6-a3*a5)
d2v/dx2=[a6*ln(1/(du/dt+a1*u+1/2)-1)-a3*ln(1/(dv/dt+a1*u+1/2)-1)]/(a2*a6-a3*a5)
Then, i think you can solve it .
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Isaac
Isaac 2013-5-20
Hi Zhang,
Sorry for the late reply. I am looking to solve this with zero flux boundary conditions.
Thanks for your help.

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