Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations

Tingting Li University of Science and Technology of China Chi-Wang Shu Brown University Mengping Zhang University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1610.25006

Journal of Scientific Computing, 70, 576-607, 2017
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 (IBVP) are treated by the simplified inverse Lax-Wendroff (SILW) 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 GKS (Gustafsson, Kreiss and Sundstr\"om) 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.
high order central difference schemes; diffusion equation; simplified inverse Lax-Wendroff procedure; stability; GKS theory; eigenvalue analysis
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@inproceedings{tingting2017stability,
  title={Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations},
  author={Tingting Li, Chi-Wang Shu, and Mengping Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011094448835989120},
  booktitle={Journal of Scientific Computing},
  volume={70},
  pages={576-607},
  year={2017},
}
Tingting Li, Chi-Wang Shu, and Mengping Zhang. Stability analysis of the inverse Lax-Wendroff boundary treatment for high order central difference schemes for diffusion equations. 2017. Vol. 70. In Journal of Scientific Computing. pp.576-607. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161011094448835989120.
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