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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(u) = u^4 D (generic function with 1 method) julia> eq = DiffusionEquation(D) ∂u/∂t = ∂(D(u)*∂u/∂r)/∂r julia> prob = DirichletProblem(eq, i=0.1, b=1) ⎧ ∂u/∂t = ∂(D(u)*∂u/∂r)/∂r, r>0,t>0 ⎨ u(r,0) = 0.1, r>0 ⎩ u(0,t) = 1.0, t>0 julia> u = solve(prob) Solution u after 10 iterations retcode: Success ub = 1.0 du/do|b = -0.28388671875000004 ui = 0.10006060603081587 julia> u(0.25, 2) # Evaluate the solution anywhere and at any time 0.9440546607878473 julia> d_dr(u, 0.25, 2) # Obtain derivatives -0.25038534184881966 julia> flux(u, 0.25, 2) # Obtain the flux 0.19888290889257723