Note on the time integration of 3D advection-reaction equations (Q1567365)

A (non-specified) advection-reaction equation is considered on 3D-domain after a spatial semidiscretization (i.e. Faedo-Galerkin approximation), which leads to an initial-value problem for large first-order differential system involving reaction/emission terms (assumed highly stiff) and spatial-differences terms (assumed considerably less stiff). Then an implicit \(A\)-stable (or better \(L\)-stable) time integration formula with an iterative approximately factorized Newton method is considered. The convergence of this iteration process is proved under a certain stability criterion.