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Write a solver to solve the Fithigh-Nagumo equations

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Old   December 14, 2014, 18:24
Question Write a solver to solve the Fithigh-Nagumo equations
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beirut
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Hello everyone,
I am new in open foam, and I want to write a solver that can solve these two equations:

D/Dt
(Phi) = nabla. A nabla(Phi) + Phi - Phi^3 - Roh + K
N D/Dt (Roh) = nabla. B nabla (Roh) + Phi - Roh

Note that D/Dt is for the transient term and nabla. nabla is for the diffusion term

These equations describe two chemical substances influencing skin pigmentation and formation of patterns of Zebra... You can see two variables (Phi and Roh) and four constants (A, K, N, B). My problem is that every equation contains the two variables so they should be solved as a system not separately. Can anyone help me to solve that problem? I need instructions about what to do? Do I have to use an existing solver and change something?
I will appreciate any help.
Thank you
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