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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Courant–Friedrichs–Lewy condition canonical | 8 |
| Courant number | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T738096 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Courant–Friedrichs–Lewy condition Context triple: [von Neumann stability analysis, relatedTo, Courant–Friedrichs–Lewy condition]
-
A.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
-
B.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
-
C.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
D.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
E.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Courant–Friedrichs–Lewy condition Target entity description: 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.
-
A.
von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
-
B.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
-
C.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
D.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
E.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
- F. None of above. chosen
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 ⓘ 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Courant–Friedrichs–Lewy condition Description of subject: 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.
Referenced by (9)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Richard Courant
this entity surface form:
Courant number