Many physical problems arising from high frequency waves, dispersive waves or Hamiltonian systems require the computations of multivalued solutions which cannot be described by the viscosity methods. In this talk I will review several recent numerical methods for such problems, including the moment methods, kinetic equations and level set methods. Applications to the semiclassical Schroedinger equation and Euler-Piosson
equations with applications to modulated electron beams in Klystrons,
and general symmetric hyperbolic systems
will be discussed.
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