Diagonizable extended backward differentiation formulas
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.