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AuthorRaed Ali, Mara'Beh
AuthorSpiteri, Raymond J.
AuthorGonzález, P.
AuthorMantas, José M.
Available date2022-09-27T05:44:47Z
Publication Date2023-01-31
Publication NameApplied Numerical Mathematics
Identifierhttp://dx.doi.org/10.1016/j.apnum.2022.08.015
CitationMara'Beh, R. A., Spiteri, R. J., González, P., & Mantas, J. M. (2022). 3-additive linear multi-step methods for diffusion-reaction-advection models. Applied Numerical Mathematics.
ISSN01689274
URIhttps://www.sciencedirect.com/science/article/pii/S0168927422002203
URIhttp://hdl.handle.net/10576/34521
AbstractSome systems of differential equations that model problems in science and engineering have natural splittings of the right-hand side into the sum of three parts, in particular, diffusion, reaction, and advection. Implicit-explicit (IMEX) methods treat these three terms with only two numerical methods, and this may not be desirable. Accordingly, this work gives a detailed study of 3-additive linear multi-step methods for the solution of diffusion-reaction-advection systems. Specifically, we construct new 3-additive linear multi-step methods that treat diffusion, reaction, and advection with separate methods. The stability of the new methods is investigated, and the order of convergence is tested numerically. A comparison of the new methods is made with some popular IMEX methods in terms of stability and performance. It is found that the new 3-additive methods have larger stability regions than the IMEX methods tested in some cases and generally outperform in terms of computational efficiency.
SponsorRaed Ali Mara'Beh, and the rest of the authors of the UGR, acknowledges the support of grant PID2020-117846GB-I00 from the Spanish government and the María de Maeztu Excellence Unit IMAG, reference CEX2020-001105-M, funded by MCIN/AEI/10.13039/501100011033/, also P. González and Raed MaraBeh acknowledges the support of the Andalusian-Spanish Research Group FQM191. Raymond J. Spiteri acknowledges support from the National Sciences and Engineering Research Council of Canada (NSERC) under Discovery Grant RGPN-2020-04467.
Languageen
PublisherElsevier
SubjectAdditive splitting methods
Linear multi-step methods
Diffusion-reaction-advection problems
IMEX
Order conditions
Linear stability analysis
Title3-additive linear multi-step methods for diffusion-reaction-advection models
TypeArticle
Pagination15-38
Volume Number183
dc.accessType Open Access


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