@article{Mara'Beh-2023-3-additive,
title = "3-additive linear multi-step methods for diffusion-reaction-advection models",
author = "Mara'Beh, Raed Ali and
Spiteri, Raymond J. and
Gonz{\'a}lez, Pedro and
Mantas, Jos{\'e} Miguel",
journal = "Applied Numerical Mathematics, Volume 183",
volume = "183",
year = "2023",
publisher = "Elsevier BV",
url = "https://gwf-uwaterloo.github.io/gwf-publications/G23-5001",
doi = "10.1016/j.apnum.2022.08.015",
pages = "15--38",
abstract = "Some 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.",
}

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<abstract>Some 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.</abstract>
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%0 Journal Article
%T 3-additive linear multi-step methods for diffusion-reaction-advection models
%A Mara’Beh, Raed Ali
%A Spiteri, Raymond J.
%A González, Pedro
%A Mantas, José Miguel
%J Applied Numerical Mathematics, Volume 183
%D 2023
%V 183
%I Elsevier BV
%F Mara'Beh-2023-3-additive
%X Some 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.
%R 10.1016/j.apnum.2022.08.015
%U https://gwf-uwaterloo.github.io/gwf-publications/G23-5001
%U https://doi.org/10.1016/j.apnum.2022.08.015
%P 15-38

##### Markdown (Informal)

[3-additive linear multi-step methods for diffusion-reaction-advection models](https://gwf-uwaterloo.github.io/gwf-publications/G23-5001) (Mara'Beh et al., GWF 2023)

##### ACL

- Raed Ali Mara'Beh, Raymond J. Spiteri, Pedro González, and José Miguel Mantas. 2023. 3-additive linear multi-step methods for diffusion-reaction-advection models.
*Applied Numerical Mathematics, Volume 183*, 183:15–38.