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On the Partial Difference Equations of Mathematical Physics
Abstract
Problems involving the classical linear partial differential equations of mathematical physics can be reduced to algebraic ones of a very much simpler structure by replacing the differentials by difference quotients on some (say rectilinear) mesh. This paper will undertake an elementary discussion of these algebraic problems, in particular of the behavior of the solution as the mesh width tends to zero. For present purposes we limit ourselves mainly to simple but typical cases, and treat them in such a way that the applicability of the method to more general difference equations and to those with arbitrarily many independent variables is made clear.
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Cited by
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Communication-Efficient and Distributed Learning Over Wireless Networks: Principles and Applications
Park, J., Samarakoon, S., Elgabli, A., Kim, J., Bennis, M., Kim, S.-L., & Debbah, M. (2021) · Proceedings of the IEEE · doi:10.1109/jproc.2021.3055679 · Cited by 25
Metadata
- Authors
- Courant, R., Friedrichs, K., & Lewy, H.
- Venue
- IBM Journal of Research and Development
- Publisher
- IBM
- Published
- 1967-03
- Volume
- 11
- Issue
- 2
- Pages
- 215-234
- ISSN
- 0018-8646 (ISSN-L)
- OpenAlex
- W4292069163
- Cited by
- 2,476
- References
- 0
- FWCI
- 0.41
- Type
- journal article
- Language
- en
- Open access
- closed
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- Courant, R., Friedrichs, K., & Lewy, H. (1967). On the Partial Difference Equations of Mathematical Physics. IBM Journal of Research and Development. https://doi.org/10.1147/rd.112.0215
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