Gaussian quadrature method with exponential fitting factor for two-parameter singularly perturbed parabolic problem.
Crank-Nicolson
Fitted operator
Gaussian quadrature
Second order interpolation
Singularly perturbed problems
Journal
BMC research notes
ISSN: 1756-0500
Titre abrégé: BMC Res Notes
Pays: England
ID NLM: 101462768
Informations de publication
Date de publication:
12 Oct 2024
12 Oct 2024
Historique:
received:
18
04
2024
accepted:
01
10
2024
medline:
13
10
2024
pubmed:
13
10
2024
entrez:
12
10
2024
Statut:
epublish
Résumé
The parabolic convection-diffusion-reaction problem is examined in this work, where the diffusion and convection terms are multiplied by two small parameters, respectively. The proposed approach is based on a fitted operator finite difference method. The Crank-Nicolson method on uniform mesh is utilized to discretize the time variables in the first step. Two-point Gaussian quadrature rule is used for further discretizing these semi-discrete problems in space, and the second order interpolation of the first derivatives is utilized. The fitting factor's value, which accounts for abrupt changes in the solution, is calculated using the theory of singular perturbations. The developed scheme is demonstrated to be second-order accurate and uniformly convergent. The proposed method's applicability is validated by two examples, which yielded more accurate results than some other methods found in the literatures.
Identifiants
pubmed: 39396021
doi: 10.1186/s13104-024-06965-8
pii: 10.1186/s13104-024-06965-8
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
304Informations de copyright
© 2024. The Author(s).
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