Experiments with an ODE solver on a multiprocessor system

A natural approach for giving a positive answer to the need of faster ODE solvers consists in the use of parallel computers or distributed systems. Unfortunately, there are only a small number of software packages available for these machines which are dedicated to ODEs. Therefore, the design of a new ODE solving environment for stiff or large ODE systems must take into account some facilities for parallel or distributed computation. We describe briefly a prototype of a solving environment for IVPs of the following form: y′(t) = f(t,y(t)), y(t0) = y0, where f : [t0,t0 + T] × Rn → Rn, y0 ε Rn, in which sequential or parallel methods can be described, tested, and compared relative to the practical problems given by the user. Numerical results are presented and interpreted. It is proved that parallel implicit methods can be used with success to generate the numerical solutions of large and sparse IVPs not only on parallel computers but also on computer networks.