2024
DOI: 10.1088/1742-5468/ad363f
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Optimal finite-differences discretization for the diffusion equation from the perspective of large-deviation theory

Naftali R Smith

Abstract: When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps Δx, Δt in space and time, respectively. By applying large-deviation theory on the discretized dynamics, we analyze the numerical errors due to the discretization, and find that the (relative) errors are especially large in regions of space where the concentration of particles is very small. We find that the choice … Show more

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