## Fronts.jl

Semi-infinite nonlinear diffusion problems in Julia
Author gerlero
Popularity
4 Stars
Updated Last
12 Months Ago
Started In
December 2020

Fronts, at the speed of Julia ⚡️

This is the (fully native) Julia version of our numerical package for nonlinear diffusion problems, also available as a Python library.

```julia> using Fronts

julia> D(c) = c^4
D (generic function with 1 method)

julia> eq = DiffusionEquation(D, symbol=:c)
∂c/∂t = ∂(D(c)*∂c/∂r)/∂r

julia> prob = DirichletProblem(eq, i=0.1, b=1)
⎧ ∂c/∂t = ∂(D(c)*∂c/∂r)/∂r, r>0,t>0
⎨ c(r,0) = 0.1, r>0
⎩ c(0,t) = 1.0, t>0

julia> c = solve(prob)
Solution c obtained after 10 iterations
cb = 1.0
dc/dϕ|b = -0.28388671875000004
ci = 0.10006060603081587

julia> c(0.25, 2) # Evaluate the solution anywhere and at any time
0.9440546607878473

julia> ∂_∂r(c, 0.25, 2) # Obtain derivatives
-0.25038534184881966

julia> flux(c, 0.25, 2) # Obtain the flux
0.19888290889257723```

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