Journal
JOURNAL OF SCIENTIFIC COMPUTING
Volume 70, Issue 2, Pages 576-607Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10915-016-0258-x
Keywords
High order central difference schemes; Diffusion equation; Simplified inverse Lax-Wendroff procedure; Stability; GKS theory; Eigenvalue analysis
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Funding
- AFOSR [F49550-12-1-0399]
- NSF [DMS-1418750]
- NSFC [11471305]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1418750] Funding Source: National Science Foundation
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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 Sundstrom 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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