Numerical integration of stiff differential equations

In many applications, the dynamics of a system can be modeled by differential equations. The study of mechanical systems (e.g. in astronomy or molecular dynamics), the analysis of electrical circuits or control theory (robotics) provide us with such problems. Often, for so-called steep problems, standard methods do not provide a correct solution in an acceptable computation time.

This summary dossier explains the phenomena that appear in stiff differential equations, using examples from chemical reactions and spatially discretized partial differential equations. The essential properties of numerical integrators for solving stiff equations are discussed (A-stability, stability domain). For general problems, implicit Runge-Kutta methods, multi-step methods (BDF) and extrapolation methods are discussed. For particular high-dimensional stiff problems, explicit methods with large stability regions, separation methods and implicit-explicit methods are also discussed. A list of public-domain computer programs is given in Documentation [Doc. AF 653] .

For references on the numerical solution of stiff differential equations, the reader may wish to consult the following general works [1] [2] [3] [4] [5] [6], mentioned in "Further reading".