Numerical algorithm for the model describing anomalous diffusion in expanding media

Abstract

We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is first established. Then we use the finite element method to discretize the Laplace operator and present error estimate of the spatial semi-discrete scheme based on the regularity of the solution; the backward Euler convolution quadrature is developed to approximate Riemann-Liouville fractional derivative and error estimates for the fully discrete scheme are established by using the continuity of solution. Finally, the numerical experiments verify the effectiveness of the algorithm.

arXiv comment28 pages

References in corpus (7)

• A new difference scheme for the time fractional diffusion equation
• Continuous-time random-walk model for anomalous diffusion in expanding media
• Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties
• Subdiffusion in an external force field
• Continuous time random walks and Fokker-Planck equation in expanding media
• Langevin dynamics for Lévy walk with memory
• The standard and the fractional Ornstein-Uhlenbeck process on a growing domain