Radiation boundary conditions for wave‐like equations

Alvin Bayliss*, Eli Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In the numerical computation of hyperbolic equations it is not practical to use infinite domains. Instead, one truncates the domain with an artificial boundary. In this study we construct a sequence of radiating boundary conditions for wave‐like equations. We prove that as the artificial boundary is moved to infinity the solution approaches the solution of the infinite domain as O(r−m−1/2) for the m‐th boundary condition. Numerical experiments with problems in jet acoustics verify the practical nature and utility of the boundary conditions.

Original languageEnglish
Pages (from-to)707-725
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Issue number6
StatePublished - Nov 1980


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