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Journal Articles Applied Mathematics Research eXpress Year : 2015

Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme

Abstract

We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step $\delta t$ and on the mesh size $\delta x$ and for $N$ - the number of realizations - reasonably large, we control this error by a term of order $\mathcal{O}(\sqrt{\delta t /N})$. We also provide some numerical experiments to confirm the error estimate, and to expose some examples of equations which can be treated by the numerical method.
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Dates and versions

hal-00800133 , version 1 (13-03-2013)

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Charles-Edouard Bréhier, Erwan Faou. Analysis of the Monte-Carlo error in a hybrid semi-Lagrangian scheme. Applied Mathematics Research eXpress, 2015, 2015 (2), pp.167-203. ⟨10.1093/amrx/abv001⟩. ⟨hal-00800133⟩
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