Abstract
Peer two-step W-methods are designed for integration of stiff initial value problems with parallelism across the method. The essential feature is that in each time step s ‘peer’ approximations are employed having similar properties. In fact, no primary solution variable is distinguished. Parallel implementation of these stages is easy since information from one previous time step is used only and the different linear systems may be solved simultaneously. This paper introduces a subclass having order s−1 where optimal damping for stiff problems is obtained by using different system parameters in different stages. Favourable properties of this subclass are uniform stability for realistic stepsize sequences and a superconvergence property which is proved using a polynomial collocation formulation. Numerical tests on a shared memory computer of a matrix-free implementation with Krylov methods are included.
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AMS subject classification (2000)
65L06, 65Y05.
Received June 2004. Revised January 2005. Communicated by Timo Eirola.
Helmut Podhaisky: The work of this author was supported by the German Academic Exchange Service, DAAD.
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Schmitt, B.A., Weiner, R. & Podhaisky, H. Multi-Implicit Peer Two-Step W-Methods for Parallel Time Integration. Bit Numer Math 45, 197–217 (2005). https://doi.org/10.1007/s10543-005-2635-y
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DOI: https://doi.org/10.1007/s10543-005-2635-y