Lax equivalence theorem

Finite Difference Methods for Hyperbolic PDEs

Published in Victor G. Ganzha, Evgenii V. Vorozhtsov, Numerical Solutions for Partial Differential Equations, 2017

Victor G. Ganzha, Evgenii V. Vorozhtsov

One of the theorems of this kind is the Lax equivalence theorem.5 It follows from these convergence results that the difference scheme chosen for the solution of an applied problem should possess the properties of the approximation and of the stability.

Density Wave Instability Verification of 1-D Computational Two-Fluid Model

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Journal Information

Published in Nuclear Science and Engineering, 2021

Krishna Chetty, Subash Sharma, John Buchanan, Martin Lopez-de-Bertodano

The more general TFM (Ref. 17) is used for nuclear reactor design-basis-accident licensing as well as a wide spectrum of other accidents and abnormal situations. However, while the TFM has the capability to simulate the DWI problem, there is no precise numerical verification of the TFM for the DWI problem at present. Verification requires consistency and convergence, according to the Lax Equivalence Theorem, and comparison with the theory of Ishii.1 The Lax Equivalence Theorem states that “for a consistent finite difference method for a well-posed linear initial value partial differential equation problem, the numerical method is convergent if and only if it is stable.”

Lax equivalence theorem

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Finite Difference Methods for Hyperbolic PDEs

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