An unconditionally stable algorithm for multiterm time fractional advection-diffusion equation with variable coefficients and convergence analysis

This paper focuses on the numerical solution of the variable coefficient multiterm time fractional advection-diffusion equation via exponential B-splines. We discretize the temporal part by using the Crank-Nicolson method and spatial part by the exponential B-splines. The unconditional stability is obtained by the Von-Neumann method. The convergence rates are also studied. Numerical simulations confirm the theoretically expected accuracy in both time and space directions. A comparative analysis with the other methods shows the superiority of the proposed algorithm.

Automated summary

This paper focuses on numerically solving the variable coefficient multiterm time fractional advection-diffusion equation using exponential B-splines. The temporal part is discretized using the Crank-Nicolson method and spatial part by exponential B-splines. The results show unconditional stability, convergence rates, and superiority over other methods in both time and space directions.