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一种显式无条件稳定格式：应用于扩散型新冠疫情模型。

An explicit unconditionally stable scheme: application to diffusive Covid-19 epidemic model.

作者信息

Nawaz Yasir, Arif Muhammad Shoaib, Abodayeh Kamaleldin, Shatanawi Wasfi

机构信息

Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000 Pakistan.

Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.

出版信息

Adv Differ Equ. 2021;2021(1):363. doi: 10.1186/s13662-021-03513-7. Epub 2021 Aug 3.

DOI:10.1186/s13662-021-03513-7
PMID:34367268
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8329645/
Abstract

An explicit unconditionally stable scheme is proposed for solving time-dependent partial differential equations. The application of the proposed scheme is given to solve the COVID-19 epidemic model. This scheme is first-order accurate in time and second-order accurate in space and provides the conditions to get a positive solution for the considered type of epidemic model. Furthermore, the scheme's stability for the general type of parabolic equation with source term is proved by employing von Neumann stability analysis. Furthermore, the consistency of the scheme is verified for the category of susceptible individuals. In addition to this, the convergence of the proposed scheme is discussed for the considered mathematical model.

摘要

提出了一种用于求解与时间相关的偏微分方程的显式无条件稳定格式。给出了该格式在求解COVID-19疫情模型中的应用。该格式在时间上是一阶精度，在空间上是二阶精度，并为所考虑类型的疫情模型提供了获得正解的条件。此外，通过冯·诺依曼稳定性分析证明了该格式对于带有源项的一般类型抛物方程的稳定性。此外，还验证了该格式对于易感个体类别的一致性。除此之外，还讨论了所提出格式对于所考虑数学模型的收敛性。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/e473/8329645/c12ea88d2c58/13662_2021_3513_Fig11_HTML.jpg
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