An efficient numerical algorithm for solving the two-dimensional fractional cable equation

Abstract

Abstract In this paper, we consider an efficient numerical algorithm for solving the two-dimensional fractional cable equation. The stability and convergency of the numerical scheme are rigorously proved by the Fourier analysis. Then we find that the convergence order is O(τ2+hx4+hy4) $O(\tau^{2}+h_{x}^{4}+h_{y}^{4})$. Finally, numerical experiments are carried out to verify the accuracy and effectiveness of the new scheme.

Keywords

• Fractional cable equation
• Fourier analysis
• Stability
• Convergence