Geodesic
Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays
Theoretical and applied mechanics, Tome 48 (2021) no. 2.

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This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor's series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.
Keywords: delay differential equation, exponentially fitted scheme, uniform convergence 
@article{TAM_2021_48_2_a6,
     author = {Mesfin Woldaregay and Worku Aniley and Gemechis Duressa},
     title = {Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays},
     journal = {Theoretical and applied mechanics},
     pages = {171 - 186},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2021},
     url = {http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a6/}
}
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Mesfin Woldaregay; Worku Aniley; Gemechis Duressa. Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays. Theoretical and applied mechanics, Tome 48 (2021) no. 2. http://geodesic.mathdoc.fr/item/TAM_2021_48_2_a6/