von Neumann stability analysis
E14978
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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| von Neumann stability analysis canonical | 3 |
| Von Neumann stability analysis | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T131675 — 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: von Neumann stability analysis Context triple: [John von Neumann, notableConcept, von Neumann stability analysis]
-
A.
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.
-
B.
Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
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C.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
D.
Differential analyzer
The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
-
E.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
- 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: von Neumann stability analysis Target entity description: 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.
-
A.
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.
-
B.
Fourier analysis
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
-
C.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
D.
Differential analyzer
The Differential Analyzer is an early analog mechanical computer designed to solve differential equations using interconnected rotating shafts and wheels.
-
E.
Navier–Stokes equations
The Navier–Stokes equations are fundamental partial differential equations in fluid mechanics that describe how the velocity field of a fluid evolves under forces like pressure and viscosity.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical method
ⓘ
numerical analysis technique ⓘ stability analysis method ⓘ |
| analyzes |
discrete evolution of error modes
ⓘ
spectral properties of difference operators ⓘ |
| appliesTo |
finite difference methods
ⓘ
linear constant-coefficient PDEs ⓘ linear partial differential equations ⓘ |
| assumes |
linearization of the numerical scheme
ⓘ
superposition of Fourier modes ⓘ |
| basedOn |
Fourier mode analysis
ⓘ
Fourier series decomposition ⓘ assumption of periodic boundary conditions ⓘ |
| criterion |
all amplification factors must have modulus less than or equal to one for stability
ⓘ
no Fourier mode may grow unbounded in time ⓘ |
| field |
computational mathematics
ⓘ
numerical analysis ⓘ partial differential equations ⓘ |
| goal |
determine stable ranges of discretization parameters
ⓘ
ensure numerical solution does not grow without bound ⓘ |
| historicalContext | developed in the mid-20th century ⓘ |
| keyConcept |
Fourier mode
ⓘ
amplification factor ⓘ stability criterion ⓘ |
| limitation |
does not directly address nonlinear stability
ⓘ
primarily applicable to linear problems ⓘ |
| namedAfter | John von Neumann ⓘ |
| relatedTo |
Courant–Friedrichs–Lewy condition
ⓘ
Lax equivalence theorem ⓘ energy method for stability ⓘ |
| requires |
discrete dispersion relation
ⓘ
representation of numerical solution as sum of complex exponentials ⓘ |
| typicalOutput |
CFL-type stability condition
ⓘ
relationship between time step and spatial grid size ⓘ time step restriction ⓘ |
| usedFor |
analyzing growth of Fourier modes in numerical methods
ⓘ
deriving stability conditions for time-marching schemes ⓘ stability analysis of finite difference schemes ⓘ stability analysis of numerical schemes for PDEs ⓘ |
| usedIn |
computational fluid dynamics
ⓘ
computational physics ⓘ engineering simulations of PDEs ⓘ numerical weather prediction ⓘ |
| usedWith |
Crank–Nicolson scheme
ⓘ
central difference schemes ⓘ explicit time-stepping schemes ⓘ implicit time-stepping schemes ⓘ upwind finite difference schemes ⓘ |
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: von Neumann stability analysis Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Von Neumann stability analysis