Name
Title | ||
|---|---|---|
A center Box method for radially symmetric solution of fractional subdiffusion equation. |
Abstract | ||
|---|---|---|
In this paper, a center Box difference method is considered for the radially symmetric solutionof fractional subdiffusion equation. By method of order reduction, the derivativeboundary condition is transformed into Dirichlet boundary condition and thus the geometricalsingularity is successfully removed from the original problem. As a matter of course, anatural discretization scheme is obtained. To investigate the stability and convergence ofthe method, we define a new norm with a weight rd -1 . Thus, the usual Sobolev inequalityis not suitable to the new norm. Therefore, we prove three new Sobolev-like embeddinginequalities which can also be applied to the other problems in polar coordinates. Then, the scheme is proved to be unconditionally stable and convergent in maximum norm with the help of the new Sobolev-like embedding inequalities. Some illustrative examples areprovided to demonstrate the theoretical results. By some comparisons, it can be seen that the natural discretization scheme is accurate and effective in physical simulations. And it can be used to both long time and short time computation. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.amc.2015.01.015 | Applied Mathematics and Computation |
Keywords | Field | DocType |
stability,convergence | Convergence (routing),Discretization,Boundary value problem,Mathematical optimization,Embedding,Mathematical analysis,Dirichlet boundary condition,Singularity,Polar coordinate system,Sobolev inequality,Mathematics | Journal |
Volume | ISSN | Citations |
257 | 0096-3003 | 3 |
PageRank | References | Authors |
0.44 | 16 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiuling Hu | 1 | 38 | 2.57 |
| Hong-Lin Liao | 2 | 3 | 0.44 |
| F. Liu | 3 | 419 | 42.86 |
| Ian Turner | 4 | 1016 | 122.29 |