A comparative study of the point implicit schemes on solving the 2D time fractional cable equation

Abstract

The time fractional cable equation is a fundamental equation used for modeling neuronal dynamics. The equation is obtained by substituting the first order time derivative in the standard equation with a Caputo fractional derivative of order α, where 0 < α < 1. In this paper, two implicit difference schemes, the fully implicit (FI) and the Crank-Nicolson (C-N) difference schemes are employed in solving the 2D time fractional cable equation (TFCE). A comparative study between these two schemes will be conducted via numerical experiments. The efficiency of the schemes in terms of accuracy and computing time will be reported and discussed.