Partitioning ODE systems with an application to air pollution models

The numerical treatment of stiff ODE systems is carried out by using implicit methods. A long sequence of nonlinear systems has to be treated when implicit methods are used. The Newton iterative method is often used in the solution of these systems. This leads to the calculation of Jacobian matrices and to the inversion of these matrices. The computational work can in some cases be reduced considerably when some kind of partitioning is used. The conditions under which the partitioning procedures can successfully be used will be studied in this paper. An example, taken from a large air pollution model, will be given to illustrate the usefulness of the theoretical results.