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

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

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...

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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
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Institution: Nanyang Technological University
Language: English
id sg-ntu-dr.10356-163727
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spelling sg-ntu-dr.10356-1637272022-12-15T03:38:32Z Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series Penent, Guillaume Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Ordinary Differential Equations Runge–Kutta Method 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. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under its Tier 2 Grant MOE-T2EP20120-0005. 2022-12-15T03:38:32Z 2022-12-15T03:38:32Z 2022 Journal Article Penent, G. & Privault, N. (2022). Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series. BIT Numerical Mathematics, 62(4), 1921-1944. https://dx.doi.org/10.1007/s10543-022-00936-w 0006-3835 https://hdl.handle.net/10356/163727 10.1007/s10543-022-00936-w 2-s2.0-85140040062 4 62 1921 1944 en MOE-T2EP20120-0005 BIT Numerical Mathematics © 2022 The Author(s), under exclusive licence to Springer Nature B.V.. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Ordinary Differential Equations
Runge–Kutta Method
spellingShingle Science::Mathematics
Ordinary Differential Equations
Runge–Kutta Method
Penent, Guillaume
Privault, Nicolas
Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Penent, Guillaume
Privault, Nicolas
format Article
author Penent, Guillaume
Privault, Nicolas
author_sort Penent, Guillaume
title Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
title_short Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
title_full Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
title_fullStr Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
title_full_unstemmed Numerical evaluation of ODE solutions by Monte Carlo enumeration of Butcher series
title_sort numerical evaluation of ode solutions by monte carlo enumeration of butcher series
publishDate 2022
url https://hdl.handle.net/10356/163727
_version_ 1753801105990483968

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