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.

Multistep, Runge-Kutta and extrapolation methods (msc 65L06)
Modelling, Analysis and Simulation [MAS]

Frank, J.E, & van der Houwen, P.J. (1999). Diagonizable extended backward differentiation formulas. Modelling, Analysis and Simulation [MAS]. CWI.