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

• Main Authors: Penent, Guillaume, Privault, Nicolas
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics; Ordinary Differential Equations; Runge–Kutta Method
• Online Access: https://hdl.handle.net/10356/163727
• Institution: Nanyang Technological University

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 certa...