Approximate factorization seems for certain problems a viable alternative to time splitting. Since a splitting error is avoided, accuracy will in general be favourable compared to time splitting methods. However, it is not clear to what extent stability is affected by factorization. Therefore we study here the effects of factorization on a simple, low order method, namely the $theta$-method. For this simple method it is possible to obtain rather precise results, showing limitations of the approximate factorization approach.

Stability and convergence of numerical methods (msc 65L20), Stability and convergence of numerical methods (msc 65M12), Method of lines (msc 65M20)
CWI
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Hundsdorfer, W. (1997). Stability of approximate factorization with $ heta $-methods. Modelling, Analysis and Simulation [MAS]. CWI.