頁籤選單縮合
題 名 | Embedded Waveform Relaxation Methods for Parabolic Partial Functional Differential Equations |
---|---|
作 者 | 劉軍; 蔣耀林; 徐洪坤; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 15:2 2011.04[民100.04] |
頁 次 | 頁829-855 |
分類號 | 314.2 |
關鍵詞 | Embedded waveform relaxation; Partial functional differential equations; Fixed and distributed delays; Superlinear convergence; Windowing technique; |
語 文 | 英文(English) |
英文摘要 | Waveform relaxation methods are decoupling or splitting methods for large scale ordinary differential equations. In this paper, we apply the meth- ods directly to semi-linear parabolic partial functional differential equations. Taking into consideration of the complicated forms of these parabolic equa- tions, we propose a kind of embedded waveform relaxation methods, which are in fact two-level waveform relaxation methods and which can also be ap- plied to some other systems. We provide explicit iterative expressions of the embedded methods and exhibit the superlinear rate of convergence on finite time intervals. We also apply the two-level idea to the functional differential equations derived from semi-discretization of the original system. The win- dowing technique is employed for the situation of long time intervals. Finally, two numerical experiments are performed to confirm our theory. |
本系統中英文摘要資訊取自各篇刊載內容。