Stability Analysis of the Inverse Lax–Wendroff Boundary Treatment for High Order Central Difference Schemes for Diffusion Equations
详细信息 查看全文
- 作者：Tingting Li ; Chi-Wang Shu ; Mengping Zhang
- 关键词：High order central difference schemes ; Diffusion equation ; Simplified inverse Lax–Wendroff procedure ; Stability ; GKS theory ; Eigenvalue analysis
- 刊名：Journal of Scientific Computing
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：70
- 期：2
- 页码：576-607
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1573-7691
- 卷排序：70
文摘
In this paper, high order central finite difference schemes in a finite interval are analyzed for the diffusion equation. Boundary conditions of the initial-boundary value problem are treated by the simplified inverse Lax–Wendroff procedure. For the fully discrete case, a third order explicit Runge–Kutta method is used as an example for the analysis. Stability is analyzed by both the Gustafsson, Kreiss and Sundström theory and the eigenvalue visualization method on both semi-discrete and fully discrete schemes. The two different analysis techniques yield consistent results. Numerical tests are performed to demonstrate and validate the analysis results.