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- W2079074770 abstract "The convergence of the Bremmer series expansion for the solution of the one-dimensional Helmholtz equation with varying wave number is investigated. It is proved that the series converges provided the quantity εσ is sufficiently small, where ε measures the relative rate of change 1/k2(dk/dx) and σ the relative total change of the wave number k. An exactly soluble example is discussed in order to show that convergence fails if the above criterion is significantly relaxed. It is shown that if the Bremmer method is applied to the calculation of the time-dependent response to an externally imposed signal, the series is convergent at any finite time after the signal is turned on." @default.
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- W2079074770 date "1967-08-01" @default.
- W2079074770 modified "2023-09-25" @default.
- W2079074770 title "Convergence of the Bremmer Series for the Spatially Inhomogeneous Helmholtz Equation" @default.
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- W2079074770 doi "https://doi.org/10.1063/1.1705399" @default.
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