Über die partiellen Differenzengleichungen der mathematischen Physik¶
Courant, R., Friedrichs, K., & Lewy, H. (1928). Über die partiellen Differenzengleichungen der mathematischen Physik. Mathematische Annalen, 100(1), 32-74.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Mechanisms¶
- Finite-Element or Cellular-Automaton Model
- A too-large time step relative to cell size violates stability limits and the solution blows up or drifts into unphysical oscillation — the Courant–Friedrichs–Lewy condition names exactly this coupling of step, cell size, and propagation speed.
This sourceDerives a stability-related condition coupling time step, spatial mesh size, and propagation speed for finite-difference solutions.
- A too-large time step relative to cell size violates stability limits and the solution blows up or drifts into unphysical oscillation — the Courant–Friedrichs–Lewy condition names exactly this coupling of step, cell size, and propagation speed.
- Stencil Computation Template
- The stencil footprint and step size, though, have to respect a stability limit,
This sourceDerives a necessary relationship between spatial and temporal step sizes for stability of a finite-difference computation.
- The stencil footprint and step size, though, have to respect a stability limit,
- Wave Superposition Simulation
- The realism of the prediction hinges on the grid being fine enough and the time step small enough to keep the march stable.
This sourceShows that hyperbolic time marching requires temporal and spatial mesh widths to satisfy stability and convergence inequalities.
- The realism of the prediction hinges on the grid being fine enough and the time step small enough to keep the march stable.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Not recorded. Neither this nor any other of the 3 citations of this work carries a recorded support check.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
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Links previously used in the corpus¶
Before the registry existed this work was also linked 1 other way.
Registry ID ref:3144f794064f · see in the full table