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

Speaker(s)

Jan Wróblewski

Affiliation

MIM UW

Date

Jan. 24, 2024, 2:15 p.m.

Room

room 5070

Seminar

Seminar of Biomathematics and Game Theory Group

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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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