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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Sem. Biomath. & Game Th.


Convergence of a cellular automata reaction-diffusion model to the PDE model

Prelegent: Jan Wróblewski

2024-01-24 14:15

Cellular automata (CA) are used to simulate physical processes with various degrees of precision, but the theoretical quantitative bounds for this precision are rarely computed. We create a stochastic CA model of reaction-diffusion process with a parameter that can increase its precision by increasing the number of molecules within. We convert the solution of this CA to a piecewise-constant function and compare it with a regular PDE solution with similar initial conditions. The main result of presented work is that, as the precision parameter increases, the CA solution converges in mean square to a certain deterministic numerical scheme, which converges to the PDE solution in the limit. This convergence may also be achieved for different stochastic CA under some conditions.