Abstract
AbstractMany processes contain phenomena on different time scales, leading to model equations with fast and small parts. There are several approaches to solve these equations, like additive Runge Kutta methods or multirate infinitesimal steps methods (MIS). Both methods make use of the additive splitting of the ODE in fast and small parts. The multiple infinitesimal step method integrates the slow part with a large macro stepsize, whereas the fast terms are solved with several smaller steps of a simpler method. The order conditions of a MIS method are derived under the assumption of the exact integration of the fast parts.We develop the multirate finite step methods (MFS). These methods are derived from the MIS methods, by taking a simple small scale integrator for the fast terms. This small scale integrator uses the same number of steps in each stage. With these assumptions, we derive the order conditions, such that the order is independent in the number of small steps. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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