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Journal Articles Mathematics of Computation Year : 2023

Tamed stability of finite difference schemes for the transport equation on the half-line

Abstract

In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numerical boundary conditions are $\ell^1$-stable but $\ell^q$-unstable for any $q > 1$. The proof relies on the accurate description of the Green's function for a particular family of finite rank perturbations of Toeplitz operators whose essential spectrum belongs to the closed unit disk and with a simple eigenvalue of modulus 1 embedded into the essential spectrum.
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Dates and versions

hal-04059973 , version 1 (05-04-2023)

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Lucas Coeuret. Tamed stability of finite difference schemes for the transport equation on the half-line. Mathematics of Computation, In press, ⟨10.1090/mcom/3901⟩. ⟨hal-04059973⟩
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