Name
Title | ||
|---|---|---|
A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients |
Abstract | ||
|---|---|---|
In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2) and computational cost of O(n3) down to n and O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.amc.2014.08.031 | Applied Mathematics and Computation |
Keywords | Field | DocType |
fast fourier transform,anomalous diffusion,circulant matrix,toeplitz matrix | Mathematical optimization,Coefficient matrix,Nonlinear system,Iterative method,Matrix (mathematics),Mathematical analysis,Fast Fourier transform,Gaussian elimination,Anomalous diffusion,Mathematics,Diffusion equation | Journal |
Volume | ISSN | Citations |
257 | 0096-3003 | 12 |
PageRank | References | Authors |
0.77 | 12 | 5 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| S. Chen | 1 | 34 | 4.52 |
| feng liu | 2 | 163 | 16.86 |
| Xiaoyun Jiang | 3 | 115 | 15.58 |
| Ian Turner | 4 | 1016 | 122.29 |
| Vo Anh | 5 | 1244 | 91.60 |