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Numerical computation of the scattering frequencies for acoustic wave equations. (English) Zbl 0643.65080
The first step of the described method is to solve the time dependent wave equation \(u_{tt}-\Delta u+q(x)u=0\) for any convenient nontrivial initial data. The second step is to fix x and calculate the exponents of the known asymptotic expansion \(u\sim \Sigma c_ jp_ j(x)\exp (is_ jt)\) from the step one discrete numerical solutions evaluated at equally spaced times. This delicate numerical procedure, previously investigated, uses a classical idea of Prony which reduces the problem to solving two systems of linear equations and finding the zeros of a polynomial of degree n. Example calculations and a discussion of accuracy complete the paper.
Reviewer: W.Ames

65Z05 Applications to the sciences
76Q05 Hydro- and aero-acoustics
35Q99 Partial differential equations of mathematical physics and other areas of application
78A45 Diffraction, scattering
35L15 Initial value problems for second-order hyperbolic equations
Full Text: DOI
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