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.
- Pub Date:
- September 2011
- Physics - Computational Physics;
- Condensed Matter - Statistical Mechanics;
- Mathematics - Numerical Analysis;
- Communications in Computational Physics, 13 (2), (2013), 502-525