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Numerical resolution of a few PDEs using Markov Chains.
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LICENSE.md
README.md
equation_1_edge_reached.ipynb
equation_1_evolution.ipynb
equation_1_proof.pdf
equation_2_cemetery_edge_reached.ipynb
equation_2_cemetery_evolution.ipynb
equation_2_cemetery_proof.pdf
equation_2_feynman_kac_edge_reached.ipynb
equation_2_feynman_kac_evolution.ipynb
equation_2_feynman_kac_proof.pdf
equation_3_edge_reached.ipynb
equation_3_evolution.ipynb
equation_3_proof.pdf

README.md

MCMCforPDEs

Description

Numerical resolution of a few PDEs using Markov Chains. We cover three differential equations with Dirichlet boundary conditions:

  • Equation 1 (Laplace equation): equation
  • Equation 2: equation
  • Equation 3: equation

For the second equation, we suggest two different methods (cemetery and Feynman-Kac). For each method we include three Jupyter notebooks:

  • The first (proof) contains a description of the method and a proof that it provides a good approximation of the equation's solution.
  • The second (edge_reached) contains the code computing and plotting an approximation of the solution.
  • The third (evolution) contains the code computing and plotting an approximation of the evolution of the associated time-dependent equation (e.g. the Heat equation for the Laplace equation).

Authors

Timothée Chauvin and JS Denain.

License

This project is under the MIT license.

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