Abstract
We generalize the extended backward differentiation formulas (EBDFs) introduced by Cash and by Psihoyios and Cash so that the system matrix in the modified Newton process can be block-diagonalized, enabling an efficient parallel implementation. The purpose of this paper is to justify the use of diagonalizable EBDFs on parallel computers and to offer a starting point for the development of a variable stepsize-variable order method. We construct methods which are L-stable up to order p = 6 and which have the same computational complexity per processor as the conventional BDF methods. Numerical experiments with the order 6 method show that a speedup factor of between 2 and 4 on four processors can be expected.
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Frank, J.E., Van Der Houwen, P.J. Diagonalizable Extended Backward Differentiation Formulas. BIT Numerical Mathematics 40, 497–512 (2000). https://doi.org/10.1023/A:1022367713296
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DOI: https://doi.org/10.1023/A:1022367713296