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dc.contributor.authorKou, Jisheng
dc.contributor.authorChen, Huangxin
dc.contributor.authorWang, Xiuhua
dc.contributor.authorSun, Shuyu
dc.date.accessioned2021-09-08T06:33:49Z
dc.date.available2021-09-08T06:33:49Z
dc.date.issued2021
dc.identifier.citationKou, J., Chen, H., Wang, X., & Sun, S. (2021). A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion. Communications on Pure & Applied Analysis, 0(0), 0. doi:10.3934/cpaa.2021094
dc.identifier.issn1553-5258
dc.identifier.doi10.3934/cpaa.2021094
dc.identifier.urihttp://hdl.handle.net/10754/671112
dc.description.abstractIn this paper, we propose an efficient numerical method for a comprehensive infection model that is formulated by a system of nonlinear coupling advection-diffusion-reaction equations. Using some subtle mixed explicit-implicit treatments, we construct a linearized and decoupled discrete scheme. Moreover, the proposed scheme is capable of preserving the positivity of variables, which is an essential requirement of the model under consideration. The proposed scheme uses the cell-centered finite difference method for the spatial discretization, and thus, it is easy to implement. The diffusion terms are treated implicitly to improve the robustness of the scheme. A semi-implicit upwind approach is proposed to discretize the advection terms, and a distinctive feature of the resulting scheme is to preserve the positivity of variables without any restriction on the spatial mesh size and time step size. We rigorously prove the unique existence of discrete solutions and positivity-preserving property of the proposed scheme without requirements for the mesh size and time step size. It is worthwhile to note that these properties are proved using the discrete variational principles rather than the conventional approaches of matrix analysis. Numerical results are also provided to assess the performance of the proposed scheme.
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.urlhttps://www.aimsciences.org/article/doi/10.3934/cpaa.2021094
dc.rightsThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure & Applied Analysis following peer review. The definitive publisher-authenticated version is available online at: http://doi.org/10.3934/cpaa.2021094
dc.titleA linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion
dc.typeArticle
dc.contributor.departmentComputational Transport Phenomena Lab
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalCommunications on Pure & Applied Analysis
dc.rights.embargodate2022-09-08
dc.eprint.versionPost-print
kaust.personSun, Shuyu
refterms.dateFOA2021-09-09T05:38:55Z


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