TAMED STABILITY OF FINITE DIFFERENCE SCHEMES FOR THE TRANSPORT EQUATION ON THE HALF-LINE

被引：0

作者：

Coeuret, Lucas ^{[1
]}

机构：

[1] Univ TOULOUSE, Inst Math TOULOUSE, UMR5219, CNRS, 118 Route Narbonne, F-31062 Toulouse 9, France

来源：

MATHEMATICS OF COMPUTATION | 2024年 / 93卷 / 347期

关键词：

Hyperbolic equations; difference approximations; stability; boundary conditions; semigroup estimates; Toeplitz operators; Lopatinskii determinant; SEMIGROUP STABILITY; CONVOLUTION POWERS; COMPLEX FUNCTIONS; APPROXIMATIONS;

D O I：

10.1090/mcom/3901

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 l(1)-stable but l(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.

引用

页码：1097 / 1151

页数：55

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