Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models
<p>Advection-diffusion-reaction (ADR) models describe transport mechanisms in fluid or solid media. They are often formulated as partial differential equations that are spatially discretized into systems of ordinary differential equations (ODEs) in time for numerical resolution. This paper inv...
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2025
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| _version_ | 1864513550075035648 |
|---|---|
| author | Raed Ali Mara'Beh (17337892) |
| author2 | J.M. Mantas (21091790) P. González (17491578) Raymond J. Spiteri (18367774) |
| author2_role | author author author |
| author_facet | Raed Ali Mara'Beh (17337892) J.M. Mantas (21091790) P. González (17491578) Raymond J. Spiteri (18367774) |
| author_role | author |
| dc.creator.none.fl_str_mv | Raed Ali Mara'Beh (17337892) J.M. Mantas (21091790) P. González (17491578) Raymond J. Spiteri (18367774) |
| dc.date.none.fl_str_mv | 2025-04-14T12:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1016/j.camwa.2025.04.002 |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Performance_comparison_of_variable-stepsize_IMEX_SBDF_methods_on_advection-diffusion-reaction_models/28795625 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Mathematical sciences Applied mathematics Numerical and computational mathematics Additive splitting methods Linear multistep methods Advection-diffusion-reaction equations Semi-implicit backward differentiation formula (SBDF) methods Variable stepsize |
| dc.title.none.fl_str_mv | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p>Advection-diffusion-reaction (ADR) models describe transport mechanisms in fluid or solid media. They are often formulated as partial differential equations that are spatially discretized into systems of ordinary differential equations (ODEs) in time for numerical resolution. This paper investigates the performance of variable stepsize, semi-implicit, backward differentiation formula (VSSBDF) methods of up to fourth order for solving ADR models employing two different implicit-explicit splitting approaches: a physics-based splitting and a splitting based on a dynamic linearization of the resulting system of ODEs, called jacobian splitting in this paper. We develop an adaptive time-stepping and error control algorithm for VSSBDF methods up to fourth order based on a step-doubling refinement technique using estimates of the local truncation errors. Through a systematic comparison between physics-based and Jacobian splitting across six ADR test models, we evaluate the performance based on CPU times and corresponding accuracy. Our findings demonstrate the general superiority of Jacobian splitting in several experiments.</p><h2>Other Information</h2> <p> Published in: Computers & Mathematics with Applications<br> License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.camwa.2025.04.002" target="_blank">https://dx.doi.org/10.1016/j.camwa.2025.04.002</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_4714ee424d465b6ad43cc5e7ec7a493e |
| identifier_str_mv | 10.1016/j.camwa.2025.04.002 |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/28795625 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction modelsRaed Ali Mara'Beh (17337892)J.M. Mantas (21091790)P. González (17491578)Raymond J. Spiteri (18367774)Mathematical sciencesApplied mathematicsNumerical and computational mathematicsAdditive splitting methodsLinear multistep methodsAdvection-diffusion-reaction equationsSemi-implicit backward differentiation formula (SBDF) methodsVariable stepsize<p>Advection-diffusion-reaction (ADR) models describe transport mechanisms in fluid or solid media. They are often formulated as partial differential equations that are spatially discretized into systems of ordinary differential equations (ODEs) in time for numerical resolution. This paper investigates the performance of variable stepsize, semi-implicit, backward differentiation formula (VSSBDF) methods of up to fourth order for solving ADR models employing two different implicit-explicit splitting approaches: a physics-based splitting and a splitting based on a dynamic linearization of the resulting system of ODEs, called jacobian splitting in this paper. We develop an adaptive time-stepping and error control algorithm for VSSBDF methods up to fourth order based on a step-doubling refinement technique using estimates of the local truncation errors. Through a systematic comparison between physics-based and Jacobian splitting across six ADR test models, we evaluate the performance based on CPU times and corresponding accuracy. Our findings demonstrate the general superiority of Jacobian splitting in several experiments.</p><h2>Other Information</h2> <p> Published in: Computers & Mathematics with Applications<br> License: <a href="http://creativecommons.org/licenses/by/4.0/" target="_blank">http://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1016/j.camwa.2025.04.002" target="_blank">https://dx.doi.org/10.1016/j.camwa.2025.04.002</a></p>2025-04-14T12:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1016/j.camwa.2025.04.002https://figshare.com/articles/journal_contribution/Performance_comparison_of_variable-stepsize_IMEX_SBDF_methods_on_advection-diffusion-reaction_models/28795625CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/287956252025-04-14T12:00:00Z |
| spellingShingle | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models Raed Ali Mara'Beh (17337892) Mathematical sciences Applied mathematics Numerical and computational mathematics Additive splitting methods Linear multistep methods Advection-diffusion-reaction equations Semi-implicit backward differentiation formula (SBDF) methods Variable stepsize |
| status_str | publishedVersion |
| title | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| title_full | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| title_fullStr | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| title_full_unstemmed | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| title_short | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| title_sort | Performance comparison of variable-stepsize IMEX SBDF methods on advection-diffusion-reaction models |
| topic | Mathematical sciences Applied mathematics Numerical and computational mathematics Additive splitting methods Linear multistep methods Advection-diffusion-reaction equations Semi-implicit backward differentiation formula (SBDF) methods Variable stepsize |