Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
Numerical Analysis
2022-08-25 v2 Numerical Analysis
Probability
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.
Keywords
Cite
@article{arxiv.2201.05998,
title = {Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series},
author = {Guillaume Penent and Nicolas Privault},
journal= {arXiv preprint arXiv:2201.05998},
year = {2022}
}