TITLE: Purely "discrete" PDEs?
QUESTION [5 upvotes]: Usually, one formulates a system of continuous PDEs and then discretizes it in order to approximately solve it.
Is there a view point that instead formulates a system of "discrete" PDEs, which therefore do not require a discretization step in order to solve it, even if some other type of reformulation may be required?

REPLY [3 votes]: You can consider cellular automata. See Cellular Automata Modeling of Physical Systems (Chopard & Droz, CUP 1998) for the application of cellular automata to modeling physical systems.