Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
We present the numerical application of a meshfree algorithm for the solution of fully nonlinear PDEs by Monte Carlo simulation using branching diffusion trees coded by the nonlinearities appearing in the equation. This algorithm is applied to the numerical solution of modified and non-Newtonian Bur...
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| Format: | Journal Article |
| Language: | English |
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2023
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| Online Access: | https://hdl.handle.net/10356/171400 |
| _version_ | 1811681848093310976 |
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| author | Nguwi, Jiang Yu Privault, Nicolas |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Nguwi, Jiang Yu Privault, Nicolas |
| author_sort | Nguwi, Jiang Yu |
| collection | NTU |
| description | We present the numerical application of a meshfree algorithm for the solution of fully nonlinear PDEs by Monte Carlo simulation using branching diffusion trees coded by the nonlinearities appearing in the equation. This algorithm is applied to the numerical solution of modified and non-Newtonian Burgers equations, and to a problem with boundary conditions in fluid dynamics, by the computation of a Poiseuille flow. Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods. |
| first_indexed | 2024-10-01T03:47:28Z |
| format | Journal Article |
| id | ntu-10356/171400 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:47:28Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1714002023-10-24T02:46:58Z Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees Nguwi, Jiang Yu Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Monte Carlo Method Branching Process We present the numerical application of a meshfree algorithm for the solution of fully nonlinear PDEs by Monte Carlo simulation using branching diffusion trees coded by the nonlinearities appearing in the equation. This algorithm is applied to the numerical solution of modified and non-Newtonian Burgers equations, and to a problem with boundary conditions in fluid dynamics, by the computation of a Poiseuille flow. Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under the Tier 1 Grant MOE2020-T1-002-047. 2023-10-24T02:46:58Z 2023-10-24T02:46:58Z 2023 Journal Article Nguwi, J. Y. & Privault, N. (2023). Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees. Japan Journal of Industrial and Applied Mathematics, 40(3), 1745-1763. https://dx.doi.org/10.1007/s13160-023-00611-9 0916-7005 https://hdl.handle.net/10356/171400 10.1007/s13160-023-00611-9 2-s2.0-85169564979 3 40 1745 1763 en MOE2020-T1-002-047 Japan Journal of Industrial and Applied Mathematics © 2023 The JJIAM Publishing Committee and Springer Nature Japan KK, part of Springer Nature. All rights reserved. |
| spellingShingle | Science::Mathematics Monte Carlo Method Branching Process Nguwi, Jiang Yu Privault, Nicolas Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title | Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title_full | Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title_fullStr | Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title_full_unstemmed | Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title_short | Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees |
| title_sort | numerical solution of the modified and non newtonian burgers equations by stochastic coded trees |
| topic | Science::Mathematics Monte Carlo Method Branching Process |
| url | https://hdl.handle.net/10356/171400 |
| work_keys_str_mv | AT nguwijiangyu numericalsolutionofthemodifiedandnonnewtonianburgersequationsbystochasticcodedtrees AT privaultnicolas numericalsolutionofthemodifiedandnonnewtonianburgersequationsbystochasticcodedtrees |