On Boundary Extrapolation and Dissipative Schemes for Hyperbolic Problems,
Abstract
This note considers dissipative, stable approximations to well-posed linear hyperbolic initial value problems in the quarter plane x > or = 0, t > or = 0. It is shown that if boundary values are determined by extrapolation, then stability is maintained. This result was first suggested by Kreiss. The proof is reviewed here using a new stability criterion for a certain family of boundary conditions due to Goldberg and Tadmor. The Lax-Wendroff scheme and other dissipative approximations are applied to a test problem. As expected from Gustafsson's rate-of-convergence theory, computations verify that if the boundary extrapolation and the difference scheme have equal order of accuracy, then this order is preserved.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1977
- Accession Number
- ADA045875
Entities
People
- Moshe Goldberg
Organizations
- University of California, Los Angeles