Abstract
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.
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We thank one of the referees for giving the remark about the alternative approach for the stability analysis at the end of the concluding remarks section.
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C.-W. Shu: Research supported by AFOSR Grant F49550-12-1-0399 and NSF Grant DMS-1418750.
M. Zhang: Research supported by NSFC Grant 11471305.
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Li, T., Shu, CW. & Zhang, M. Stability Analysis of the Inverse Lax–Wendroff Boundary Treatment for High Order Central Difference Schemes for Diffusion Equations. J Sci Comput 70, 576–607 (2017). https://doi.org/10.1007/s10915-016-0258-x
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DOI: https://doi.org/10.1007/s10915-016-0258-x