Lax equivalence theorem
E87776
The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Lax equivalence theorem canonical | 4 |
| Lax–Richtmyer equivalence theorem | 1 |
| Lax–Richtmyer theorem | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T738097 — 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: Lax equivalence theorem Context triple: [von Neumann stability analysis, relatedTo, Lax equivalence theorem]
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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.
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B.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
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C.
Euler equations
The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
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D.
local existence and uniqueness theorem
The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
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E.
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.
- 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: Lax equivalence theorem Target entity description: The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
-
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.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
-
C.
Euler equations
The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
-
D.
local existence and uniqueness theorem
The local existence and uniqueness theorem is a fundamental result in differential equations that guarantees, under suitable conditions, a single solution passing through a given initial point, valid in some neighborhood of that point.
-
E.
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.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
theorem in numerical analysis ⓘ |
| alsoKnownAs |
Lax–Richtmyer equivalence theorem
ⓘ
linked to:
Lax equivalence theorem
|
| appliesTo |
discretizations on nonuniform grids
ⓘ
discretizations on uniform grids ⓘ well-posed linear initial value problems ⓘ |
| assumes |
finite difference discretization
ⓘ
linear problem ⓘ well-posed problem ⓘ |
| clarifies | relationship between stability and convergence ⓘ |
| concerns |
consistency of numerical schemes
ⓘ
convergence of numerical schemes ⓘ finite difference methods ⓘ linear initial value problems ⓘ stability of numerical schemes ⓘ |
| domain |
linear partial differential equations
ⓘ
time-dependent problems ⓘ |
| field |
numerical analysis
ⓘ
partial differential equations ⓘ |
| formalizes | equivalence of stability plus consistency with convergence for linear well-posed problems ⓘ |
| hasConsequence |
for linear well-posed problems, convergence analysis can focus on stability and consistency
ⓘ
stability is necessary for convergence of consistent schemes ⓘ |
| historicalContext | 20th-century numerical analysis ⓘ |
| implies | convergence of a finite difference scheme under stability and consistency ⓘ |
| mathematicalNature | equivalence theorem ⓘ |
| namedAfter | Peter Lax ⓘ |
| provenBy | Peter Lax ⓘ |
| relatedTo |
Cauchy problem
ⓘ
Lax stability condition ⓘ finite difference scheme ⓘ von Neumann stability analysis ⓘ |
| relatesConcept |
consistency
ⓘ
convergence ⓘ stability ⓘ well-posedness ⓘ |
| states | for a well-posed linear initial value problem, stability and consistency of a finite difference scheme imply convergence ⓘ |
| typicalApplication |
numerical solution of hyperbolic PDEs
ⓘ
numerical solution of parabolic PDEs ⓘ |
| usedIn |
analysis of numerical schemes for PDEs
ⓘ
design of stable numerical methods ⓘ verification of convergence of discretization 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: Lax equivalence theorem Description of subject: The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lax equivalence theorem
linked to: Lax equivalence theorem