An exponentially fitted spline method for singularly perturbed parabolic convection-diffusion problems with large time delay

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Naol Tufa Negero
Gemechis File Duressa

Abstract

This paper deals with the numerical solutions of singularly perturbed parabolic convection-diffusion problems with a large delay in time. An exponentially fitted scheme is formulated using cubic splines method in equally-spaced grids. As the delay parameter is larger than the perturbation parameter, a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted cubic spline method based on Crank-Nicolson's discretization scheme is developed. The obtained scheme is conditionally stable. Parameter-uniform error estimates are derived and it is shown that the method is ε-uniformly convergent of second-order accurate in both temporal direction and spatial direction. The proposed method provides more accurate solutions than an upwind finite difference scheme in a piecewise uniform mesh.  

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How to Cite
Negero, N. T., & Duressa, G. F. (2022). An exponentially fitted spline method for singularly perturbed parabolic convection-diffusion problems with large time delay. Tamkang Journal of Mathematics. Retrieved from https://journals.math.tku.edu.tw/index.php/TKJM/article/view/3983
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Papers
Author Biography

Naol Tufa Negero, Department of Mathematics, Wollega University

Naol Tufa Negero is a faculty memeber and PhD scholar at the Department of Mathematics, Wollega University.