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- Lax_equivalence_theorem abstract "In numerical analysis, the Lax equivalence theorem is the fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations. It states that for a consistent finite difference method for a well-posed linear initial value problem, the method is convergent if and only if it is stable.The importance of the theorem is that while convergence of the solution of the finite difference method to the solution of the partial differential equation is what is desired, it is ordinarily difficult to establish because the numerical method is defined by a recurrence relation while the differential equation involves a differentiable function. However, consistency—the requirement that the finite difference method approximate the correct partial differential equation—is straightforward to verify, and stability is typically much easier to show than convergence (and would be needed in any event to show that round-off error will not destroy the computation). Hence convergence is usually shown via the Lax equivalence theorem.Stability in this context means that a matrix norm of the matrix used in the iteration is at most unity, called (practical) Lax-Richtmyer stability. Often a von Neumann stability analysis is substituted for convenience, although von Neumann stability only implies Lax-Richtmyer stability in certain cases.This theorem is due to Peter Lax. It is sometimes called the Lax–Richtmyer theorem, after Peter Lax and Robert D. Richtmyer.".
- Lax_equivalence_theorem wikiPageExternalLink search?id=lax-equivalence-theorem1.
- Lax_equivalence_theorem wikiPageExternalLink chap5.pdf.
- Lax_equivalence_theorem wikiPageID "7018809".
- Lax_equivalence_theorem wikiPageRevisionID "541715716".
- Lax_equivalence_theorem hasPhotoCollection Lax_equivalence_theorem.
- Lax_equivalence_theorem subject Category:Numerical_differential_equations.
- Lax_equivalence_theorem subject Category:Theorems_in_analysis.
- Lax_equivalence_theorem type Abstraction100002137.
- Lax_equivalence_theorem type Communication100033020.
- Lax_equivalence_theorem type DifferentialEquation106670521.
- Lax_equivalence_theorem type Equation106669864.
- Lax_equivalence_theorem type MathematicalStatement106732169.
- Lax_equivalence_theorem type Message106598915.
- Lax_equivalence_theorem type NumericalDifferentialEquations.
- Lax_equivalence_theorem type Proposition106750804.
- Lax_equivalence_theorem type Statement106722453.
- Lax_equivalence_theorem type Theorem106752293.
- Lax_equivalence_theorem type TheoremsInAnalysis.
- Lax_equivalence_theorem comment "In numerical analysis, the Lax equivalence theorem is the fundamental theorem in the analysis of finite difference methods for the numerical solution of partial differential equations.".
- Lax_equivalence_theorem label "Lax equivalence theorem".
- Lax_equivalence_theorem label "Teorema de Equivalência de Lax".
- Lax_equivalence_theorem label "Théorème de Lax".
- Lax_equivalence_theorem label "Äquivalenzsatz von Lax".
- Lax_equivalence_theorem label "ラックスの等価定理".
- Lax_equivalence_theorem sameAs Äquivalenzsatz_von_Lax.
- Lax_equivalence_theorem sameAs Théorème_de_Lax.
- Lax_equivalence_theorem sameAs ラックスの等価定理.
- Lax_equivalence_theorem sameAs Teorema_de_Equivalência_de_Lax.
- Lax_equivalence_theorem sameAs m.0h0l5q.
- Lax_equivalence_theorem sameAs Q256303.
- Lax_equivalence_theorem sameAs Q256303.
- Lax_equivalence_theorem sameAs Lax_equivalence_theorem.
- Lax_equivalence_theorem wasDerivedFrom Lax_equivalence_theorem?oldid=541715716.
- Lax_equivalence_theorem isPrimaryTopicOf Lax_equivalence_theorem.