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Numerical solution of the high frequency asymptotic expansion for the scalar wave equation. (English) Zbl 0836.65099
Authors’ abstract: New numerical methods are derived for calculation of high-frequency asymptotic expansion of the scalar wave equation. The nonlinear partial differential equations defining the terms in the expansion are approximated directly rather than via ray tracing. High resolution numerical algorithms are used to handle discontinuities and new devices are introduced to represent the multivalued character of the solution.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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