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I would like to know if anyone knows how to solve non-linear coupled PDEs numerically or can point me to a text book/reference which can explain how to do so. I am most familiar with finite difference methods, so it would be preferable if I could get an algorithm which used a finite difference method, but I am flexible.

The system of equations are

∂b/∂t = dΔb + εnb - a(b,n)b

∂s/∂t = a(b,n)b

∂n/∂t = Δn - nb

where b(x,t), s(x,t), and n(x,t) are all functions of space and time; a(b,n) is some decreasing function of b and n (something simple, but not constant); ε and d are constants. The initial and boundary conditions are will be either dirichlet or neumann and the initial conditions are simple.

Any help would be appreciated. Thank you for your time.