Fitted computational method for solving singularly perturbed small time lag problem.
Accurate numerical method
Exponentially fitted method
Stability and uniform convergence
Journal
BMC research notes
ISSN: 1756-0500
Titre abrégé: BMC Res Notes
Pays: England
ID NLM: 101462768
Informations de publication
Date de publication:
11 Oct 2022
11 Oct 2022
Historique:
received:
10
06
2022
accepted:
07
09
2022
entrez:
11
10
2022
pubmed:
12
10
2022
medline:
12
10
2022
Statut:
epublish
Résumé
An accurate exponentially fitted numerical method is developed to solve the singularly perturbed time lag problem. The solution to the problem exhibits a boundary layer as the perturbation parameter approaches zero. A priori bounds and properties of the continuous solution are discussed. The backward-Euler method is applied in the time direction and the higher order finite difference method is employed for the spatial derivative approximation. An exponential fitting factor is induced on the difference scheme for stabilizing the computed solution. Using the comparison principle, the stability of the method is examined and analyzed. It is proved that the method converges uniformly with linear order of convergence. To validate the theoretical findings and analysis, two test examples are given. Comparison is made with the results available in the literature. The proposed method has better accuracy than the schemes in the literature.
Identifiants
pubmed: 36221103
doi: 10.1186/s13104-022-06202-0
pii: 10.1186/s13104-022-06202-0
pmc: PMC9552406
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
318Informations de copyright
© 2022. The Author(s).
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