Numerical solution for a non-Fickian diffusion in a periodic potential
  Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented. 
Ad\'erito Ara\'ujo, Amal K. Das, Cid\'alia Neves, Erc\'ilia Sousa
physics.comp-ph cond-mat.stat-mech math.NA