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

Abstract

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.

Keywords

• Time-fractional convection-dominated diffusion equation
• Tailored finite point method
• Exponential basis function
• Cauchy–Schwarz inequality