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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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2024
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| Online Access: | https://hdl.handle.net/10356/175826 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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