A second-order accurate numerical method for the two-dimensional fractional diffusion equation |
| |
Authors: | Charles Tadjeran Mark M. Meerschaert |
| |
Affiliation: | aDepartment of Physics, University of Nevada, Reno, USA;bDepartment of Statistics and Probability Michigan State University East Lansing, MI 48824-1027 USA |
| |
Abstract: | Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method. |
| |
Keywords: | Two-dimensional fractional partial differential equation Extrapolated Crank– Nicolson method Numerical solution for superdiffusion Alternating direction implicit methods Second-order accurate method for fractional diffusion |
本文献已被 ScienceDirect 等数据库收录! |