Geodesic
Robust numerical method for singularly perturbed parabolic differential equations with negative shifts
Filomat, Tome 35 (2021) no. 7, p. 2383

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DOI

This paper deals with numerical treatment of singularly perturbed parabolic differential equations having delay on the zeroth and first order derivative terms. The solution of the considered problem exhibits boundary layer behaviour as the perturbation parameter tends to zero. The equation is solved using θ-method in temporal discretization and exponentially fitted finite difference method in spatial discretization. The stability of the scheme is proved by using solution bound technique by constructing barrier functions. The parameter uniform convergence analysis of the scheme is carried out and it is shown to be accurate of order O(N −2 N −1 +cε + (∆t) 2) for the case θ = 1 2 , where N is the number of mesh points in spatial discretization and ∆t is the mesh size in temporal discretization. Numerical examples are considered for validating the theoretical analysis of the scheme
DOI : 10.2298/FIL2107383W
Classification : 65M06, 65M12, 65M15
Keywords: Boundary layer, θ-Method, Exponentially fitted method, Singularly perturbed problem 
Mesfin Mekuria Woldaregay; Gemechis File Duressa. Robust numerical method for singularly perturbed parabolic differential equations with negative shifts. Filomat, Tome 35 (2021) no. 7, p. 2383 . doi: 10.2298/FIL2107383W
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     author = {Mesfin Mekuria Woldaregay and Gemechis File Duressa},
     title = {Robust numerical method for singularly perturbed parabolic differential equations with negative shifts},
     journal = {Filomat},
     pages = {2383 },
     year = {2021},
     volume = {35},
     number = {7},
     doi = {10.2298/FIL2107383W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2107383W/}
}
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