Abstract
Explicit parallel two-step peer methods use s stages with essentially identical properties. They are quite efficient in solving standard nonstiff initial value problems and may obtain a parallel speed-up near s on s processors for expensive problems. The two-step structure requires s − 1 initial approximations which have been computed by one-step methods in earlier versions. We now present a self-contained starting procedure using parallel Euler steps in the initial interval. Low order error terms introduced by this step are eliminated by special coefficient sets increasing the order to s after s − 2 time steps. An estimate for the initial stepsize is discussed, as well. Parallel OpenMP experiments with realistic problems demonstrate the efficiency compared to standard codes.
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Schmitt, B.A., Weiner, R. Parallel start for explicit parallel two-step peer methods. Numer Algor 53, 363–381 (2010). https://doi.org/10.1007/s11075-009-9267-2
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DOI: https://doi.org/10.1007/s11075-009-9267-2