A Chebyshev/radiation function pseudospectral method for wave scattering

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Abstract
Wave scattering from a potential well or barrier cannot be solved via a standard pseudospectral method. The reason is that none of the usual infinite interval basis sets can model the incoming and outgoing waves. In this article, it is shown that by constructing special ‘‘radiation functions’’ the transmission and reflection coefficients may be computed with exponential accuracy. This problem is ideally suited to pseudospectral methods because either the reflection or transmission coefficient is an exponential function of the wavenumber k. For k≫1, the overall wave field must be computed to many decimal places of accuracy to calculate the exponentially small coefficient with any precision at all.

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