On the iota-delta function: a link between cellular automata and partial differential equations for modeling advection–dispersion from a constant source

Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow...

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Bibliographic Details
Published in:The Journal of supercomputing 2017-02, Vol.73 (2), p.700-712
Main Authors: Ozelim, Luan Carlos de S. M., Cavalcante, André Luís B., Baetens, Jan M.
Format: Article
Language:English
Subjects:
Cellular automata
Compilers
Computer Science
Interpreters
Processor Architectures
Programming Languages
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Summary:Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow and both share features with two-dimensional CAs. One-dimensional CAs, on the other hand, seem to have been neglected for modeling physical phenomena. In the present paper, we demonstrate that some one-dimensional CAs are equivalent to a stable linear finite difference scheme used to solve advection–diffusion partial differential equations (PDEs) by relying on the so-called iota-delta representation. Consequently, this work shows an important link between continuous and discrete models in general, and PDEs and CAs more in particular.
ISSN:0920-8542
1573-0484
DOI:10.1007/s11227-016-1795-7