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

Prelegent(ci)

Jan Wróblewski

Afiliacja

MIM UW

Termin

24 stycznia 2024 14:15

Pokój

p. 5070

Seminarium

Seminarium Zakładu Biomatematyki i Teorii Gier

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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.

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