An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics (Q1335656)

Systems of ordinary differential equations (ODEs) describing chemical kinetics problems are considered. Many applications, such as those from air pollution modeling, give rise to a system of partial differential equations of the advection-diffusion-reaction type in which the ODE system occurs as the reaction part. Splitting is a popular approach for solving this kind of problems. Splitting involves the numerical integration of the ODE system at every grid point of the mesh for each step of the operator splitting method. The so-called pseudo-steady-state approximation (PSSA) is applied. For a number of stiff ODEs from atmospheric chemistry a simple, easy-to-use PSSA solver is compared with two state-of-the-art solvers from the stiff ODE field, the implicit Runge-Kutta code, developed by \textit{E. Hairer} and \textit{G. Wanner} [Solving ordinary differential equations. II: Stiff and differential-algebraic problems (1991; Zbl 0729.65051)] and the implicit backward differentiation code, developed by \textit{L. R. Petzold} [cf. \textit{K. E. Brenan, S. L. Campbell} and \textit{L. R. Petzold}, Numerical solution of initial-value problems in differential-algebraic equations (1989; Zbl 0699.65057)]. It is shown that in most cases the implicit codes can be made more efficient, even for the low accuracy range that is of interest for reactive flow problems.