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add RandomTamedEM() solver for RODEs #501

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merged 2 commits into from
Sep 8, 2022

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@rmsrosa rmsrosa commented Sep 7, 2022

This implements the RODE equivalent of the "Tamed Euler" SDE solver proposed in Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients by Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden.

This scheme, for a RODE $dX_t/dt = f(t, X_t, Y_t)$, with noise $Y_t$, is an explicit scheme consisting of the time steps
$$X_{t_{j+1}}^n = X_{t_j}^n + \frac{\Delta t f(t_j, X_{t_j}, Y_{t_j})}{1 + \Delta t ||f(t_j, X_{t_j}, Y_{t_j})||}$$

@ChrisRackauckas ChrisRackauckas merged commit 914a509 into SciML:master Sep 8, 2022
@rmsrosa rmsrosa deleted the random_tamed_em branch September 8, 2022 09:56
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