Stable, high-order discretization for evolution of the wave equation in 1 + 1 dimensions

We carry forward the approach of Alpert, Greengard, and Hagstrom to construct stable high-order explicit discretizations for the wave equation in one space and one time dimension. They presented their scheme as an integral form of the Lax–Wendroff method. Our perspective is somewhat different from t...

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Bibliographic Details
Published in:Journal of computational physics 2004-03, Vol.194 (2), p.395-408
Main Authors: Visher, John, Wandzura, Stephen, White, Amanda
Format: Article
Language:English
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Physics
Small-cell problem
Stability
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Summary:We carry forward the approach of Alpert, Greengard, and Hagstrom to construct stable high-order explicit discretizations for the wave equation in one space and one time dimension. They presented their scheme as an integral form of the Lax–Wendroff method. Our perspective is somewhat different from theirs; our focus is on the discretization of the evolution formula rather than on its form (integral, differential, etc.). A key feature of our approach is the independent computation of three discretizations, one for bulk (away from boundaries) propagation, one for propagation near boundaries, and a projection operator to enforce boundary conditions. This is done in a way that is straightforward to extend to more space dimensions.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2003.09.028