A note on operator splitting in a stiff linear case

This note is concerned with the numerical technique of operator splitting for initial value problems. Using a stiff linear ODE system as model problem, error bounds are derived for standard 1st- and 2nd-order splitting methods. The analysis focuses on deriving bounds independent of stiffness. The aim is to study the influence of stiffness on accuracy. Attention is paid to the influence of the splitting sequence on the splitting error and to the order reduction phenomenon.