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*Correspondence: muhammad.abbas@uos.edu.pk 2Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan Full list of author information is available at the end of the article Abstract In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

Novel finite point approach for solving time-fractional convection-dominated diffusion equations