Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series

2022/01/16 by Guillaume Penent, Penent, Guillaume, Nicolas Privault +1
Decision Sciences · Physics and Astronomy · #05C05 #34-04 #34A25 #65C05 #65L06 #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Scientific Research and Discoveries #Simulation Techniques and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2201.05998

openalex publication_date 2022/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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