A comparison of AMF- and Krylov-methods in Matlab for large stiff ODE systems

For the efficient solution of large stiff systems resulting from semidiscretization of multi-dimensional partial differential equations two methods using approximate matrix factorizations (AMF) are discussed. In extensive numerical tests of Reaction Diffusion type implemented in Matlab they are compared with integration methods using Krylov techniques for solving the linear systems or to approximate exponential matrices times a vector. The results show that for low and medium accuracy requirements AMF methods are superior. For stringent tolerances peer methods with Krylov are more efficient.