An analysis of operator splitting techniques in the stiff case
Operator splitting methods are widely used in many applications, such as air pollution modeling, combustion, and reactive flows. The author regards the case where the evolution equations to be simulated are stiff. He considers systems with two operators: a stiff one and a non-stiff one. For example, a linear evolution system under a singular perturbation has the form \[ {{d z}\over{d t}} = \Biggl({A\over \varepsilon} + B \Biggr) z,\quad z(0) = z_0, \] where \(\varepsilon\) is a small positive parameter. The author shows some splitting schemes for solving of the evolution systems (``first-order'', ``second-order'' schemes). The ``first-order'' scheme has the form \[ \begin{aligned} {{d z^*}\over{d t}} = B^* z^*,\quad z^*(0) = z_0, &\quad \text{on }[0,\Delta t],\\ {{d z^{**}}\over{d t}} = B^* z^{**},\quad z^{**}(0) = z^*(\Delta t), &\quad \text{on }[0,\Delta t],\end{aligned} \] where the final value is given by \(z^{**}(\Delta t)\). The main results deals with the choice of the sequential order for the operators: the stiff operator must always be last in the splitting scheme.
scientific article; zbMATH DE number 1471799
scientific article