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

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-10-04 DOI:10.1090/mcom/3901

Lucas Coeuret

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引用次数: 0

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 ℓ 1 \ell ^1 -stable but ℓ q \ell ^q -unstable for any q > 1 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 1 embedded into the essential spectrum.

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半线上输运方程有限差分格式的驯服稳定性

本文证明了在精确的谱假设下，具有数值边界条件的正半线上的标量左向输运方程的有限差分近似对任意q >都是稳定的，但不稳定的;1 >该证明依赖于对一类特定的Toeplitz算子的有限秩扰动的格林函数的精确描述，这些算子的本质谱属于封闭的单位圆盘，并且在本质谱中嵌入了一个模数为11的简单特征值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.