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

• المؤلفون الرئيسيون: Penent, Guillaume, Privault, Nicolas
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2022
• الموضوعات: Science::Mathematics; Ordinary Differential Equations; Runge–Kutta Method
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/163727

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...