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On the boundedness stepsizes-coefficients of a-bdf methods

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dc.contributor.author Baleanu, Dumitru
dc.contributor.author Khalsaraei, Mohammad Mehdizadeh
dc.contributor.author Shokri, Ali
dc.contributor.author Kaveh, Kamal
dc.date.accessioned 2022-11-11T11:37:27Z
dc.date.available 2022-11-11T11:37:27Z
dc.date.issued 2022
dc.identifier.citation Baleanu, Dumitru...at all (2022). "On the boundedness stepsizes-coefficients of a-bdf methods", AIMS Mathematics, Vol. 7, No. 2, pp. 1562-1579. tr_TR
dc.identifier.issn 2473-6988
dc.identifier.uri http://hdl.handle.net/20.500.12416/5863
dc.description.abstract Physical constraints must be taken into account in solving partial differential equations (PDEs) in modeling physical phenomenon time evolution of chemical or biological species. In other words, numerical schemes ought to be devised in a way that numerical results may have the same qualitative properties as those of the theoretical results. Methods with monotonicity preserving property possess a qualitative feature that renders them practically proper for solving hyperbolic systems. The need for monotonicity signifies the essential boundedness properties necessary for the numerical methods. That said, for many linear multistep methods (LMMs), the monotonicity demands are violated. Therefore, it cannot be concluded that the total variations of those methods are bounded. This paper investigates monotonicity, especially emphasizing the stepsize restrictions for boundedness of A-BDF methods as a subclass of LMMs. A-stable methods can often be effectively used for stiff ODEs, but may prove inefficient in hyperbolic equations with stiff source terms. Numerical experiments show that if we apply the A-BDF method to Sod’s problem, the numerical solution for the density is sharp without spurious oscillations. Also, application of the A-BDF method to the discontinuous diffusion problem is free of temporal oscillations and negative values near the discontinuous points while the SSP RK2 method does not have such properties. © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0). tr_TR
dc.language.iso eng tr_TR
dc.relation.isversionof 10.3934/math.2022091 tr_TR
dc.rights info:eu-repo/semantics/openAccess tr_TR
dc.subject A-BDF Method tr_TR
dc.subject Linear Multistep Method tr_TR
dc.subject Method of Lines tr_TR
dc.subject Monotonicity tr_TR
dc.subject Total-Variation-Bounded tr_TR
dc.subject Total-Variation-Diminishing tr_TR
dc.title On the boundedness stepsizes-coefficients of a-bdf methods tr_TR
dc.type article tr_TR
dc.relation.journal AIMS Mathematics tr_TR
dc.contributor.authorID 56389 tr_TR
dc.identifier.volume 7 tr_TR
dc.identifier.issue 2 tr_TR
dc.identifier.startpage 1562 tr_TR
dc.identifier.endpage 1579 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü tr_TR


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