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Particle method approximation of oscillatory solutions to hyperbolic differential equations. (English) Zbl 0675.65093
The errors for particle methods are not of dissipative or dispersive type, rather, they are errors in the approximation of the characteristics and in the approximation of lower-order terms. It is shown theoretically and with numerical experiments that these errors do not accumulate in the same way as in standard difference schemes when applied to problems with oscillatory solutions. Highly oscillatory solutions to the Broadwell and variable coefficient Carleman models are considered. Homogeneous results are given and the approximations of more general systems are discussed.
Reviewer: L.G.Vulkov

MSC:
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35L60 First-order nonlinear hyperbolic equations
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