A novel fitted numerical scheme for time-fractional singularly perturbed convection-diffusion problems with a delay in time via cubic $B$-spline approach

Aniley, Worku Tilahun; Duressa, Gemechis File

doi:10.22124/jmm.2023.25969.2303

A novel fitted numerical scheme for time-fractional singularly perturbed convection-diffusion problems with a delay in time via cubic $B$-spline approach

Document Type : Research Article

Authors

Department of Mathematics, Jimma University, Jimma, Ethiopia

10.22124/jmm.2023.25969.2303

Abstract

This paper presents a uniformly convergent numerical scheme for time-fractional singularly perturbed convection-diffusion problem with delay in time. The time-fractional derivative is considered in the Caputo sense and treated using the implicit Euler method. Then, a uniformly convergent numerical scheme based on cubic $B$-spline method is developed along the spatial direction. The technique is proved rigorously for parameter-uniform convergence. By a numerical experimentation, it is also validated that the computational result agrees with the theoretical expectation and it is also more accurate than some existing numerical methods.

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