2026-04-20T16:10:20Zhttps://riubu.ubu.es/oai/request

oai:riubu.ubu.es:10259/79692023-11-10T01:05:39Zcom_10259_6229com_10259_4534com_10259.4_106com_10259_2604col_10259_6230

Alonso Mallo, Isaías b7d0b785-aec5-43ae-9e55-0f408ac2880e 600 Reguera López, Nuria 470 600 0000-0002-6219-5531 2023-11-09T10:35:22Z 2023-11-09T10:35:22Z 2024-03 0377-0427 http://hdl.handle.net/10259/7969 10.1016/j.cam.2023.115629 When applied to stiff problems, the effective order of convergence of general linear methods is governed by their stage order, which is less than or equal to the classical order of the method. This produces an order reduction phenomenon, present in all general linear methods except those with high stage order, in a manner similar to that observed in other time integrators with internal stages. In this paper, we investigate the order reduction which arises when general linear methods are used as time integrators when using the method of lines for solving numerically initial boundary value problems with time dependent boundary values. We propose a technique, based on making an appropriate choice of the boundary values for the internal stages, with which it is possible to recover one unit of order, as we prove in this work. As expected, this implies a considerable improvement for the general linear methods suffering order reduction. Moreover, numerical experiments show that the improvement is not only in these cases, but that, even when the order reduction is not expected, the size of the errors is drastically reduced by using the technique proposed in this paper. This research has been supported by project PGC2018-101443-B-100, Ministerio de Ciencia, Innovación y Universidades (Spain) and by Junta de Castilla y León (Grant numbers VA169P20 and VA193P20). eng Elsevier Journal of Computational and Applied Mathematics. 2024, V. 439, 115629 https://doi.org/10.1016/j.cam.2023.115629 Atribución-NoComercial 4.0 Internacional http://creativecommons.org/licenses/by-nc/4.0/ info:eu-repo/semantics/openAccess Order reduction General linear methods Initial boundary value problems Matemáticas Mathematics Avoiding order reduction phenomenon for general linear methods when integrating linear problems with time dependent boundary values info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Journal of Computational and Applied Mathematics 439 THUMBNAIL Alonso-jcam_2024.pdf.jpg Alonso-jcam_2024.pdf.jpg IM Thumbnail image/jpeg 4967 https://riubu.ubu.es/bitstream/10259/7969/4/Alonso-jcam_2024.pdf.jpg 55951cbe086181a6743394c357885eb8 MD5 4 LICENSE license.txt license.txt text/plain; charset=utf-8 999 https://riubu.ubu.es/bitstream/10259/7969/3/license.txt b295bcbce42e2caabeb0c623d3860c06 MD5 3 CC-LICENSE license_rdf license_rdf application/rdf+xml; charset=utf-8 914 https://riubu.ubu.es/bitstream/10259/7969/2/license_rdf 24013099e9e6abb1575dc6ce0855efd5 MD5 2 ORIGINAL Alonso-jcam_2024.pdf Alonso-jcam_2024.pdf application/pdf 397048 https://riubu.ubu.es/bitstream/10259/7969/1/Alonso-jcam_2024.pdf 37caac5ce0c87866dd6f43c7a98c6672 MD5 1 10259/7969 oai:riubu.ubu.es:10259/7969 2023-11-10 02:05:39.687 Repositorio Institucional de la Universidad de Burgos bubrep@ubu.es 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