Rosenbrock-type methods with Inexact AMF for the time integration of advection–diffusion–reaction PDEs

摘要

The numerical integration of PDEs of Advection–Diffusion–Reaction type in several spatial variables in the MoL framework is considered. The spatial discretization is based on Finite Differences and the time integration is carried out by using splitting techniques applied to Rosenbrock-type methods. The focus here is to provide a way of making some refinements to the usual Approximate Matrix Factorization (AMF) when it is applied to some well-known Rosenbrock-type methods. The proposed AMF-refinements provide new methods in a natural way and some of these methods belong to the class of the W-methods. Interesting stability properties of the resulting methods are proved and a few numerical experiments on some important non-linear PDE problems with applications in Physics are carried out.