Analysis of a fourth-order compact $ \theta $-method for delay parabolic equations

Autor:	Lili Li, Boya Zhou, Huiqin Wei, Fengyan Wu
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	delay parabolic equations high-order numerical stability error bounds compact $ \theta $-method Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 32, Iss 4, Pp 2805-2823 (2024)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2024127?viewType=HTML
Popis:	The upper bounds for the powers of the iteration matrix derived via a numerical method are intimately related to the stability analysis of numerical processes. In this paper, we establish upper bounds for the norm of the nth power of the iteration matrix derived via a fourth-order compact $ \theta $-method to obtain the numerical solutions of delay parabolic equations, and thus present conclusions about the stability properties. We prove that, under certain conditions, the numerical process behaves in a stable manner within its stability region. Finally, we illustrate the theoretical results through the use of several numerical experiments.
Databáze:	Directory of Open Access Journals
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