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


Department of Mathematics, Jimma University, Jimma, Ethiopia


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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