Computation of oscillatory solutions to partial differential equations. (English) Zbl 0626.65085

Engquist, Björn

Nonlinear hyperbolic problems, Proc. Adv. Res. Workshop, St. Etienne/France 1986, Lect. Notes Math. 1270, 10-22 (1987).

[For the entire collection see Zbl 0623.00008.]
Numerical approximations of hyperbolic partial differential equations with oscillatory solutions are studied. Convergence is analyzed in the practical case for which the continuous 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 continuous and the corresponding numerical models converge to the same homogenized limit as the frequency in the oscillation increases.

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45	Initial value problems for first-order hyperbolic systems

Keywords:

oscillatory solutions; particle method; semilinear problems

Citations:

Zbl 0623.00008