A splitting uniformly convergent method for one-dimensional parabolic singularly perturbed convection-diffusion systems
Fecha
2023Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
Impacto
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10.1016/j.apnum.2022.09.012
Resumen
In this paper we deal with solving robustly and efficiently one-dimensional linear parabolic
singularly perturbed systems of convection-diffusion type, where the diffusion parameters
can be different at each equation and even they can have different orders of magnitude.
The numerical algorithm combines the classical upwind finite difference scheme to
discretize in space and the fractional imp ...
[++]
In this paper we deal with solving robustly and efficiently one-dimensional linear parabolic
singularly perturbed systems of convection-diffusion type, where the diffusion parameters
can be different at each equation and even they can have different orders of magnitude.
The numerical algorithm combines the classical upwind finite difference scheme to
discretize in space and the fractional implicit Euler method together with an appropriate
splitting by components to discretize in time. We prove that if the spatial discretization
is defined on an adequate piecewise uniform Shishkin mesh, the fully discrete scheme is
uniformly convergent of first order in time and of almost first order in space. The technique
used to discretize in time produces only tridiagonal linear systems to be solved at each
time level; thus, from the computational cost point of view, the method we propose is
more efficient than other numerical algorithms which have been used for these problems.
Numerical results for several test problems are shown, which corroborate in practice both
the uniform convergence and the efficiency of the algorithm. [--]
Materias
Fractional Euler method,
Shishkin meshes,
Splitting by components,
Uniform convergence,
Upwind scheme,
Weakly coupled parabolic systems
Editor
Elsevier
Publicado en
Applied Numerical Mathematics 183 (2023) 317–332
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute of Smart Cities - ISC
Versión del editor
Entidades Financiadoras
The authors thank the referees for their valuable suggestions which have helped to improve the presentation of this paper. This research was partially supported by the project MTM2017-83490-P, the Aragon Government and European Social Fund (group E24-17R ) and the Public University of Navarre, project PRO-UPNA 6158 .