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Title: Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
Authors: Penent, Guillaume
Privault, Nicolas
Keywords: Science::Mathematics
Issue Date: 2022
Source: Penent, G. & Privault, N. (2022). Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series. BIT Numerical Mathematics, 62(4), 1921-1944.
Project: MOE-T2EP20120-0005
Journal: BIT Numerical Mathematics
Abstract: We present an algorithm for the numerical solution of ordinary differential equations by random enumeration of the Butcher trees used in the implementation of the Runge–Kutta method. Our Monte Carlo scheme allows for the direct numerical evaluation of an ODE solution at any given time within a certain interval, without iteration through multiple time steps. In particular, this approach does not involve a discretization step size, and it does not require the truncation of Taylor series.
ISSN: 0006-3835
DOI: 10.1007/s10543-022-00936-w
Rights: © 2022 The Author(s), under exclusive licence to Springer Nature B.V.. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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