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000084687 005__ 20220621094623.0
000084687 0247_ $$2doi$$a10.1016/j.cam.2018.10.033
000084687 0248_ $$2sideral$$a109551
000084687 037__ $$aART-2019-109551
000084687 041__ $$aeng
000084687 100__ $$0(orcid)0000-0003-1263-1996$$aClavero, C.$$uUniversidad de Zaragoza
000084687 245__ $$aAn efficient numerical method for singularly perturbed time dependent parabolic 2D convection–diffusion systems
000084687 260__ $$c2019
000084687 5060_ $$aAccess copy available to the general public$$fUnrestricted
000084687 5203_ $$aIn this paper we deal with solving efficiently 2D linear parabolic singularly perturbed systems of convection–diffusion type. We analyze only the case of a system of two equations where both of them feature the same diffusion parameter. Nevertheless, the method is easily extended to systems with an arbitrary number of equations which have the same diffusion coefficient. The fully discrete numerical method combines the upwind finite difference scheme, to discretize in space, and the fractional implicit Euler method, together with a splitting by directions and components of the reaction–convection–diffusion operator, to discretize in time. Then, if the spatial discretization is defined on an appropriate piecewise uniform Shishkin type mesh, the method is uniformly convergent and it is first order in time and almost first order in space. The use of a fractional step method in combination with the splitting technique to discretize in time, means that only tridiagonal linear systems must be solved at each time level of the discretization. Moreover, we study the order reduction phenomenon associated with the time dependent boundary conditions and we provide a simple way of avoiding it. Some numerical results, which corroborate the theoretical established properties of the method, are shown.
000084687 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17R$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859-P
000084687 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000084687 590__ $$a2.037$$b2019
000084687 591__ $$aMATHEMATICS, APPLIED$$b43 / 260 = 0.165$$c2019$$dQ1$$eT1
000084687 592__ $$a0.87$$b2019
000084687 593__ $$aComputational Mathematics$$c2019$$dQ2
000084687 593__ $$aApplied Mathematics$$c2019$$dQ2
000084687 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000084687 700__ $$aJorge, J. C.
000084687 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000084687 773__ $$g354 (2019), 431-444$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427
000084687 8564_ $$s689941$$uhttps://zaguan.unizar.es/record/84687/files/texto_completo.pdf$$yVersión publicada
000084687 8564_ $$s143953$$uhttps://zaguan.unizar.es/record/84687/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000084687 909CO $$ooai:zaguan.unizar.es:84687$$particulos$$pdriver
000084687 951__ $$a2022-06-21-09:40:11
000084687 980__ $$aARTICLE