Courant–Friedrichs–Lewy condition
E87775
The Courant–Friedrichs–Lewy condition is a fundamental stability criterion in numerical analysis that restricts the time step size in discretized partial differential equations to ensure convergence of the computed solution.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
criterion in numerical analysis
→
mathematical concept → numerical stability condition → |
| alsoKnownAs |
CFL condition
→
|
| appliesPrimarilyTo |
explicit schemes rather than implicit schemes
→
|
| appliesTo |
discretized partial differential equations
→
explicit time-stepping schemes → finite difference methods → finite volume methods → |
| assumes |
finite propagation speed of information
→
|
| category |
condition for convergence
→
stability criterion → |
| characterizes |
maximum stable time step
→
|
| consequenceOfViolation |
divergence of numerical solution
→
numerical instability → |
| defines |
upper bound on Courant number
→
|
| field |
computational mathematics
→
numerical analysis → partial differential equations → |
| hasParameter |
Courant number
→
|
| implies |
information must not travel more than one spatial cell per time step
→
|
| influences |
choice of time step in simulations
→
computational cost of time-dependent simulations → |
| involves |
discretization in space
→
discretization in time → |
| isNecessaryFor |
convergence of many explicit finite difference schemes
→
|
| namedAfter |
Hans Lewy
→
Kurt Friedrichs NERFINISHED → Richard Courant → |
| publishedIn |
paper on finite difference methods for PDEs
→
|
| purpose |
ensure convergence of numerical solution
→
ensure numerical stability → restrict time step size → |
| relatedConcept |
Lax equivalence theorem
→
stability region of numerical scheme → von Neumann stability analysis → |
| relatesTo |
characteristic speeds of PDE
→
spatial grid size → time step size → wave propagation speed → |
| typicalForm |
c·Δt/Δx ≤ C_max
→
|
| usedIn |
computational fluid dynamics
→
computational wave propagation → hyperbolic partial differential equations → numerical weather prediction → shock-capturing schemes → |
| yearProposed |
1928
→
|
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
Richard Courant
→
|
notableWork |
|
von Neumann stability analysis
→
|
relatedTo |