Parallel implicit predictor corrector methods

The performance of parallel codes for the solution of initial value problems is usually strongly sensitive to the dimension of the continuous problem. This is due to the overhead related to the exchange of information among the processors and motivates the problem of minimizing the amount of communications. According to this principle, we define the so called Parallel Implicit Predictor Corrector Methods and in this class we derive A-stable, L-stable and numerically zero-stable formulas. The latter property refers to the zero-stability condition of a given formula when roundoff errors are introduced in its coefficients due to their representation in finite precision arithmetic. Some numerical experiment show the potentiality of this approach