Diagonalizable Extended Backward Differentiation Formulas.

摘要

We generalize the extended backward differentiation formulas (EBDFs) introduced by Cash and by Psihoyios and Cash such that the system matrix in the modified Newton process can be block-diagonalized. This enables an efficient parallel implementation. We construct methods which are L-stable up to order p=6 with the same computational complexity per processor as the conventional BDF methods. Numerical experiments with the order 6 method show that a speedup factor between 2 and 4 on four processors can be expected.