反应-扩散模型的统一分析及其在Barkley模型螺旋波动力学中的应用

IF 0.9 Q2 MATHEMATICS Arabian Journal of Mathematics Pub Date : 2023-02-27 DOI:10.1007/s40065-023-00423-2

Yahya Alnashri, Hasan Alzubaidi

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引用次数: 0

摘要

应用梯度离散化方法（GDM），对非线性方程组进行了综合数值分析，称为反应-扩散模型。该分析仅使用三个性质，就提供了与GDM一致的几种一致和非一致数值格式的收敛结果。作为该分析的应用，设计了反应-扩散模型的混合模拟混合（HMM）方法，并建立了其收敛性。使用HMM方法进行的数值实验有助于研究巴克利模型中螺旋波的产生，以及波与产生介质边界相互作用时的行为方式。

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A unified analysis for reaction–diffusion models with application to the spiral waves dynamics of the Barkley model

Applying the gradient discretisation method (GDM), the paper develops a comprehensive numerical analysis for nonlinear equations called the reaction–diffusion model. Using only three properties, this analysis provides convergence results for several conforming and non-conforming numerical schemes that align with the GDM. As an application of this analysis, the hybrid mimetic mixed (HMM) method for the reaction–diffusion model is designed, and its convergence is established. Numerical experiments using the HMM method are presented to facilitate the study of the creation of spiral waves in the Barkley model and the ways in which the waves behave when interacting with the boundaries of their generating medium.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.