Name
Title | ||
|---|---|---|
Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart. |
Abstract | ||
|---|---|---|
The solution of a Caputo time fractional diffusion equation of order 0<α<1 is expressed in terms of the solution of a corresponding integer order diffusion equation. We demonstrate a linear time mapping between these solutions that allows for accelerated computation of the solution of the fractional order problem. In the context of an N-point finite difference time discretisation, the mapping allows for an improvement in time computational complexity from O(N2) to O(Nα), given a precomputation of O(N1+αlnN). The mapping is applied successfully to the least squares fitting of a fractional advection–diffusion model for the current in a time-of-flight experiment, resulting in a computational speed up in the range of one to three orders of magnitude for realistic problem sizes. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.jcp.2014.11.023 | Journal of Computational Physics |
Keywords | Field | DocType |
Caputo time fractional advection–diffusion equation,Finite difference methods,Anomalous diffusion mapping,Time of flight experiment | Least squares,Discretization,Mathematical optimization,Mathematical analysis,Finite difference,Finite difference method,Fractional calculus,Brownian motion,Time complexity,Mathematics,Diffusion equation | Journal |
Volume | Issue | ISSN |
282 | C | 0021-9991 |
Citations | PageRank | References |
2 | 0.39 | 15 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter W. Stokes | 1 | 2 | 0.39 |
| Bronson Philippa | 2 | 9 | 1.53 |
| Wayne Read | 3 | 2 | 0.39 |
| Ronald D. White | 4 | 2 | 0.39 |