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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Nanyang Technological University
2024
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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 |
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NTU Library |
| continent |
Asia |
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Singapore Singapore |
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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 |