Abstract
Numerical approximations of hyperbolic partial differential equations with oscillatory solutions are studied. Convergence is analyzed in the practical case for which the continous solution is not well resolved on the computational grid. Averaged difference approximations of linear problems and particle method approximations of semilinear problems are presented. Highly oscillatory solutions to the Carleman and Broadwell models are considered. The continous and the corresponding numerical models converge to the same homogenized limit as the frequency in the oscillation increases.
Research supported by NSF Grant No. DMS85-03294, ARO Grant No. DAAG29-85-K-0190, NASA Consortium Agreement No. NCA2-IR360-403.
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© 1987 Springer-Verlag
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Engquist, B. (1987). Computation of oscillatory solutions to partial differential equations. In: Carasso, C., Serre, D., Raviart, PA. (eds) Nonlinear Hyperbolic Problems. Lecture Notes in Mathematics, vol 1270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078314
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DOI: https://doi.org/10.1007/BFb0078314
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