On the relation between elementary partial difference equations and partial differential equations

Annals of Pure and Applied Logic 92 (3):235-265 (1998)

Abstract
The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential equations, both of first and second order. We thus obtain straightforward discretizations and continuizations, even avoiding change of variables. In fact, we create intermediary objects: partial difference equations with S-continuous solutions, which have both discrete and continuous properties
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DOI 10.1016/s0168-0072(98)00006-2
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Nonstandard Measure Theory and its Applications.Nigel J. Cutland - 1983 - Journal of Symbolic Logic 54 (1):290-291.
Extended Use of IST.I. P. Van den Berg - 1992 - Annals of Pure and Applied Logic 58 (1):73-92.
From Discrete to Continuous Time.H. Jerome Keisler - 1991 - Annals of Pure and Applied Logic 52 (1-2):99-141.

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