Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals
文献类型：期刊论文
| 作者 | Zhang, Wenbiao1; Yi, Ming2 |
| 刊名 | ADVANCES IN DIFFERENCE EQUATIONS
 |
| 出版日期 | 2016-08-25 |
| 关键词 | fractional diffusion equation anomalous diffusion Sturm-Liouville problem implicit numerical scheme robustness |
| 英文摘要 | Classical diffusion theory is widely applied in natural science and has made a great achievement. However, the phenomenon of anomalous diffusion in discontinuous media (fractal, porous, etc.) shows that classical diffusion theory is no longer suitable. The differential equations with fractional order have recently been proved to be powerful tools for describing anomalous diffusion. Nevertheless, the analysis methods and numerical methods for fractional differential equations are still in the stage of exploration. In the paper, we consider the Sturm-Liouville problem and the numerical method of a fractional sub-diffusion equation with Dirichlet condition, respectively. We have given the series solution of equation and proved the stability and the convergence of the implicit numerical scheme. It is found that the numerical results are in satisfactory agreement with the analytical solution. Through the robustness analysis, it is also found that the diffusion processes on fractals are more sensitive to the spectral dimension than to the anomalous diffusion exponent. |
| WOS标题词 | Science & Technology ; Physical Sciences |
| 类目[WOS] | Mathematics, Applied ; Mathematics |
| 研究领域[WOS] | Mathematics |
| 关键词[WOS] | ANOMALOUS DIFFUSION ; DIFFERENTIAL-EQUATIONS ; DISORDERED MEDIA ; MELLIN TRANSFORM ; RANDOM-WALKS ; ORDER ; DERIVATIVES |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000382277200001 |
| 源URL | [http://ir.wipm.ac.cn/handle/112942/9503]  |
| 专题 | 武汉物理与数学研究所_数学物理与应用研究部 |
| 作者单位 | 1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 2.Huazhong Agr Univ, Dept Phys, Coll Sci, Wuhan 430070, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhang, Wenbiao,Yi, Ming. Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals[J]. ADVANCES IN DIFFERENCE EQUATIONS,2016. |
| APA | Zhang, Wenbiao,&Yi, Ming.(2016).Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals.ADVANCES IN DIFFERENCE EQUATIONS. |
| MLA | Zhang, Wenbiao,et al."Sturm-Liouville problem and numerical method of fractional diffusion equation on fractals".ADVANCES IN DIFFERENCE EQUATIONS (2016). |
入库方式： OAI收割
来源：武汉物理与数学研究所
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