Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains
文献类型：期刊论文
| 作者 | Ma, HP; Sun, WW; Tang, T |
| 刊名 | SIAM JOURNAL ON NUMERICAL ANALYSIS
 |
| 出版日期 | 2005 |
| 卷号 | 43期号:1页码:58-75 |
| 关键词 | Hermite spectral method time-dependent scaling stability convergence |
| ISSN号 | 0036-1429 |
| DOI | 10.1137/S0036142903421278 |
| 英文摘要 | Hermite spectral methods are investigated for linear diffusion equations and nonlinear convection-diffusion equations in unbounded domains. When the solution domain is unbounded, the diffusion operator no longer has a compact resolvent, which makes the Hermite spectral methods unstable. To overcome this difficulty, a time-dependent scaling factor is employed in the Hermite expansions, which yields a positive bilinear form. As a consequence, stability and spectral convergence can be established for this approach. The present method plays a similar role in the stability of the similarity transformation technique proposed by Funaro and Kavian [Math. Comp., 57 (1991), pp. 597-619]. However, since coordinate transformations are not required, the present approach is more efficient and is easier to implement. In fact, with the time-dependent scaling the resulting discretization system is of the same form as that associated with the classical (straightforward but unstable) Hermite spectral method. Numerical experiments are carried out to support the theoretical stability and convergence results. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000230502600004 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1216]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Ma, HP |
| 作者单位 | 1.Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China 2.City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 4.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ma, HP,Sun, WW,Tang, T. Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2005,43(1):58-75. |
| APA | Ma, HP,Sun, WW,&Tang, T.(2005).Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains.SIAM JOURNAL ON NUMERICAL ANALYSIS,43(1),58-75. |
| MLA | Ma, HP,et al."Hermite spectral methods with a time-dependent scaling for parabolic equations in unbounded domains".SIAM JOURNAL ON NUMERICAL ANALYSIS 43.1(2005):58-75. |
入库方式： OAI收割
来源：数学与系统科学研究院
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