Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees

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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Main Authors: Nguwi, Jiang Yu, Privault, Nicolas
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Monte Carlo Method
Branching Process
Online Access:https://hdl.handle.net/10356/171400
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.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.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Monte Carlo Method
Branching Process
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
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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Nguwi, Jiang Yu
Privault, Nicolas
format Article
author Nguwi, Jiang Yu
Privault, Nicolas
author_sort Nguwi, Jiang Yu
title 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_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_sort numerical solution of the modified and non-newtonian burgers equations by stochastic coded trees
publishDate 2023
url https://hdl.handle.net/10356/171400
_version_ 1781793741629030400

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