000168461 001__ 168461
000168461 005__ 20260205155159.0
000168461 0247_ $$2doi$$a10.3934/math.2026076
000168461 0248_ $$2sideral$$a147879
000168461 037__ $$aART-2026-147879
000168461 041__ $$aeng
000168461 100__ $$aShiromani, Ram
000168461 245__ $$aAn efficient numerical method to solve 2D parabolic singularly perturbed coupled systems of convection-diffusion type with multi-parameters on a Bakhvalov–Shishkin mesh
000168461 260__ $$c2026
000168461 5060_ $$aAccess copy available to the general public$$fUnrestricted
000168461 5203_ $$aThis study addresses the efficient solution of a class of 2D parabolic singularly perturbed weakly coupled systems of convection-diffusion type. In the model problem, small positive parameters appear in both the diffusion and the convection terms. We assume that the diffusion parameters can be distinct, but the convection parameter remains the same for both equations. Then, for sufficiently small values of the parameters, overlapping boundary layers appear on the boundary of the spatial domain. To solve the problem, a numerical method is employed that combines the implicit Euler scheme, defined on a uniform mesh, with the upwind scheme for spatial discretization. Then, if the spatial discretization is carried out on an adequate nonuniform Bakhvalov–Shishkin (BS) mesh, the fully discrete scheme attains uniform convergence, with respect to all perturbation parameters; moreover, it has first-order accuracy in both temporal and spatial variables. Note that the construction of the BS mesh depends on the value and the ratio between the diffusion and the convection parameters, and special generating functions are needed to construct them. Numerical experiments illustrating the performance of the algorithm for some test problems are showed, which corroborate the uniform convergence of the method in agreement with the theoretical results.
000168461 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00
000168461 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000168461 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000168461 700__ $$0(orcid)0000-0003-1263-1996$$aClavero, Carmelo$$uUniversidad de Zaragoza
000168461 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000168461 773__ $$g11, 1 (2026), 1820-1856$$tAIMS Mathematics$$x2473-6988
000168461 8564_ $$s6073334$$uhttps://zaguan.unizar.es/record/168461/files/texto_completo.pdf$$yVersión publicada
000168461 8564_ $$s1881922$$uhttps://zaguan.unizar.es/record/168461/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000168461 909CO $$ooai:zaguan.unizar.es:168461$$particulos$$pdriver
000168461 951__ $$a2026-02-05-14:37:03
000168461 980__ $$aARTICLE