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Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

  • Adérito Araújo (a1), Amal K. Das (a2), Cidália Neves (a1) (a3) and Ercília Sousa (a1)

Abstract

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.

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Corresponding author.Email:ecs@mat.uc.pt

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Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

  • Adérito Araújo (a1), Amal K. Das (a2), Cidália Neves (a1) (a3) and Ercília Sousa (a1)

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