Extrapolation methods and nonlinear transformations for applied mathematics,theoretical chemistry and molecular physics

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Highly oscillatory integrals play a major role in various applications, e.g. quantum chemistry, image analysis, electrodynamics, computerized tomography and fluid mechanics. Traditional quadrature rules have failed in the accurate and rapid numerical evaluation of these integrals. Few classes of extrapolation methods are well suited for highly oscillatory integrals, notably the D and G transformations. However, the application of these methods can be extremely difficult and require a large amount of calculation. The development of new algorithms for the computation of these methods for highly oscillatory integrals is critical.