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

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. [ABSTRACT FROM AUTHOR]