An iterated Radau method for time-dependent PDEs

Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : Systems of m PDEs of Adv-Diff-React type have the following form, where the dependent variables (unknowns) are u = (u j (x, t)) m j=1 : ∂ ∂t u j + ∇ · (a j u j) = ∇ · (D j ∇u j) + f j , These PDEs model a lot of important phenomena, see These PDEs model a lot of important phenomena, see These PDEs model a lot of important phenomena, see These PDEs model a lot of important phenomena, see These PDEs model a lot of important phenomena, see After semi-discretization in space we get the IVP: y ′ (t) = f (t, y(t)), y(t 0) = y 0 , t ∈ [t 0 , t end ], y ∈ R M , where M is often quite large. For instance, M = N d when using Finite Difference methods with N lines in each spatial variable (d could be the number of spatial variables) After semi-discretization in space we get the IVP: y ′ (t) = f (t, y(t)), y(t 0) = y 0 , t ∈ [t 0 , t end ], y ∈ R M , where M is often quite large. For instance, M = N d when using Finite Difference methods with N lines in each spatial variable (d could be the number of spatial variables) • Stiffness in J = ∂f /∂(t, y) comes from three sources, since N ≥ 100 is usual and realistic After semi-discretization in space we get the IVP: y ′ (t) = f (t, y(t)), y(t 0) = y 0 , t ∈ [t 0 , t end ], y ∈ R M , where M is often quite large. For instance, M = N d when using Finite Difference methods with N lines in each spatial variable (d could be the number of spatial variables) • Stiffness in J = ∂f /∂(t, y) comes from three sources, since N ≥ 100 is usual and realistic Diffusion terms provide a wide range of negative eigenvalues scattered on the negative real axis. After semi-discretization in space we get the IVP: y ′ (t) = f (t, y(t)), y(t 0) = y 0 , t ∈ [t 0 , t end …