Parallel Methods for Systems of Ordinary Differential Equations

Considerable attention has been devoted recently to the development of eecient parallel algorithms for the numerical solution of initial value ordinary diierential equations of the form: y 0 = f(t; y); y(t 0) = y 0 f : IR IR m) IR m : (1) An example that gives an idea of the magnitude of some of the problems involved is the modeling of long-range transport of air pollutants in the atmosphere 23]. A relatively simple model generates a system of 267,264 ODEs; to study seasonal variations in the pollutants, the system must be solved over a long time scale. Clearly, such problems cannot be solved in reasonable time without some exploitation of concurrency. In attempts to solve (1), three types of parallelism have been identiied: (i) parallelism across the method, (ii) parallelism across the system (space),