Figure 4

Propagation of the discontinuities of the solution to model (4) and the effect of the mesh refinement and the filtering procedure. Left: Solution n(t, z) of model (4) for t = 120 (hours) with the best-fit parameters estimated for data set 2. Dashed lines indicate positions of the discontinuities of the exact solution: $z_j^{\ast }$ = $z_0^{\ast }$ - j log₁₀ γ, j = 0, 1, ..., 10, $z_0^{\ast }$ ≈ 2.58, γ ≈ 1.71. Right (top): The effect of the mesh refinement on the computed solution in a neighborhood of the discontinuity at z ≈ 2.347. Dashed, solid and dot-dashed curves indicate the solution computed using the mesh size N = 500, 1000, 2000, respectively. Right (bottom): The effect of the filtering procedure: the solution computed with and without the filtering (dashed, respectively solid curves). N = 1000.