Numerical Investigation of the Fractal Mobile/Immobile Transport Model
with Caputo and Caputo-Fabrizio Fractional Derivatives using Finite
difference/Spectral Approximations
Abstract
This paper discusses a spectral collocation method for numerically
solving linear and nonlinear fractal Mobile/Immobile transport model
with Caputo and Caputo-Fabrizio fractional derivatives. In the time
direction, a finite difference scheme is used to approximate the
differential term. Also, for space discretization, we apply the
Chebyshev-spectral method. The unconditional stability and convergence
of the proposed method are investigated, which provides the theoretical
basis of the proposed method for solving the considered equation.
Finally, some numerical experiments are considered to examine the
efficiency and applicability of it in the sense of accuracy and
convergence ratio.