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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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/163727 |
| _version_ | 1811682604018040832 |
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| author | Penent, Guillaume Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Penent, Guillaume Privault, Nicolas |
| author_sort | Penent, Guillaume |
| collection | NTU |
| 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. |
| first_indexed | 2024-10-01T03:59:28Z |
| format | Journal Article |
| id | ntu-10356/163727 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:59:28Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-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. |
| 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 |
| title | 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_short | 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 |
| topic | Science::Mathematics Ordinary Differential Equations Runge–Kutta Method |
| url | https://hdl.handle.net/10356/163727 |
| work_keys_str_mv | AT penentguillaume numericalevaluationofodesolutionsbymontecarloenumerationofbutcherseries AT privaultnicolas numericalevaluationofodesolutionsbymontecarloenumerationofbutcherseries |