Survey of the stability of linear finite difference equations
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The Lax theorem states that stability and consistency imply convergence.
“Fortunately, the Lax theorem [36,37] states that stability and consistency implies convergence.”
From The Dirac equation as a quantum walk: higher dimensions, observational convergence (2014) · cites this paper as [36]
Cited by
Sorted by citations
Thermal convection with large viscosity variations
Torrance, K. E., & Turcotte, D. L. (1971) · Journal of Fluid Mechanics · doi:10.1017/s002211207100096x · Cited by 270 · see citing works
The Dirac equation as a quantum walk: higher dimensions, observational convergence
Arrighi, P., Nesme, V., & Forets, M. (2014) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/47/46/465302 · Cited by 72 · see citing works
- Authors
- Lax, P. D., & Richtmyer, R. D.
- Venue
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Published
- 1956-05
- Volume
- 9
- Issue
- 2
- Pages
- 267-293
- ISSN
- 0010-3640 (ISSN-L)
- 1097-0312
- OpenAlex
- W1983078963
- Cited by
- 826
- References
- 0
- Citations by year
- 2026: 21 · 2025: 33 · 2024: 28 · 2023: 32 · 2022: 33 · 2021: 28 · 2020: 41 · 2019: 27 · 2018: 33 · 2017: 33 · 2016: 23 · 2015: 29 · 2014: 28 · 2013: 38 · 2012: 24
- FWCI
- 7.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Communications on Pure and Applied Mathematics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Differential Equations and Numerical Methods
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Keywords
- stability, recurrence relations, numerical stability
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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