An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion

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creativework.keywordsCancer cells migration, Conser-vation laws, Evolution, Finite difference method, Positivity preserving
creativework.publisherMDPIen
dc.contributor.authorKolev M.K.
dc.contributor.authorKoleva M.N.
dc.contributor.authorVulkov L.G.
dc.date.accessioned2024-12-04T13:38:25Z
dc.date.accessioned2024-12-04T13:46:58Z
dc.date.available2024-12-04T13:38:25Z
dc.date.available2024-12-04T13:46:58Z
dc.date.issued2022-01-01
dc.description.abstractIn this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary differential equation. The unknowns represent concentrations or densities that cannot be negative. Widely used approximations, such as difference schemes, can produce negative solutions because of truncation errors and can become unstable. We propose a new difference scheme that guarantees the positivity of the numerical solution for arbitrary mesh step sizes. It has explicit and fast performance even for nonlinear reaction terms that consist of sums of positive and negative functions. The numerical examples illustrate the simplicity and efficiency of the method. A numerical simulation of a model of cancer migration is also discussed.
dc.identifier.doi10.3390/math10010131
dc.identifier.issn2227-7390
dc.identifier.scopusSCOPUS_ID:85122104737en
dc.identifier.urihttps://rlib.uctm.edu/handle/123456789/1552
dc.language.isoen
dc.source.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85122104737&origin=inward
dc.titleAn Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion
dc.typeArticle
oaire.citation.issue1
oaire.citation.volume10
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