Probabilistic numerical solution of wave equations with polynomial non-linearity

Probabilistic numerical solution of wave equations with polynomial non-linearity

We propose a Monte Carlo solution to the wave equations with polynomial non-linearity. Writing the probabilistic representation of the Monte Carlo solution, we are able to show its expected value retrieves the Duhamel’s solution of the wave equation. Based on a stochastically dominating branching...

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Main Author: Chan, Joshua Juan Yin
Other Authors: Nicolas Privault
Format: Final Year Project
Language:English
Published: Nanyang Technological University 2024
Subjects:
Mathematical Sciences
Partial differential equations
Wave equations
Duhamel’s solution
Monte Carlo method
Branching process
Stochastic dominance
Progeny problem
Online Access:https://hdl.handle.net/10356/175826
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1758262024-05-13T15:36:53Z Probabilistic numerical solution of wave equations with polynomial non-linearity Chan, Joshua Juan Yin Nicolas Privault School of Physical and Mathematical Sciences NPRIVAULT@ntu.edu.sg Mathematical Sciences Partial differential equations Wave equations Duhamel’s solution Monte Carlo method Branching process Stochastic dominance Progeny problem We propose a Monte Carlo solution to the wave equations with polynomial non-linearity. Writing the probabilistic representation of the Monte Carlo solution, we are able to show its expected value retrieves the Duhamel’s solution of the wave equation. Based on a stochastically dominating branching process, we construct the proof of finding the probability generating function of the progeny problem, from which we are able to recover a quantitative estimate on the sufficient conditions for integrability. Bachelor's degree 2024-05-08T02:45:39Z 2024-05-08T02:45:39Z 2024 Final Year Project (FYP) Chan, J. J. Y. (2024). Probabilistic numerical solution of wave equations with polynomial non-linearity. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/175826 https://hdl.handle.net/10356/175826 en application/pdf Nanyang Technological University
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Mathematical Sciences
Partial differential equations
Wave equations
Duhamel’s solution
Monte Carlo method
Branching process
Stochastic dominance
Progeny problem
spellingShingle Mathematical Sciences
Partial differential equations
Wave equations
Duhamel’s solution
Monte Carlo method
Branching process
Stochastic dominance
Progeny problem
Chan, Joshua Juan Yin
Probabilistic numerical solution of wave equations with polynomial non-linearity
description We propose a Monte Carlo solution to the wave equations with polynomial non-linearity. Writing the probabilistic representation of the Monte Carlo solution, we are able to show its expected value retrieves the Duhamel’s solution of the wave equation. Based on a stochastically dominating branching process, we construct the proof of finding the probability generating function of the progeny problem, from which we are able to recover a quantitative estimate on the sufficient conditions for integrability.
author2 Nicolas Privault
author_facet Nicolas Privault
Chan, Joshua Juan Yin
format Final Year Project
author Chan, Joshua Juan Yin
author_sort Chan, Joshua Juan Yin
title Probabilistic numerical solution of wave equations with polynomial non-linearity
title_short Probabilistic numerical solution of wave equations with polynomial non-linearity
title_full Probabilistic numerical solution of wave equations with polynomial non-linearity
title_fullStr Probabilistic numerical solution of wave equations with polynomial non-linearity
title_full_unstemmed Probabilistic numerical solution of wave equations with polynomial non-linearity
title_sort probabilistic numerical solution of wave equations with polynomial non-linearity
publisher Nanyang Technological University
publishDate 2024
url https://hdl.handle.net/10356/175826
_version_ 1814047219142098944

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