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Efficient integration for a class of highly oscillatory integrals. (English) Zbl 1246.65045
The paper is devoted to the construction and error analysis of methods for the numerical computation of oscillatory integrals with Jacobi weight functions. The first method is based on developing an asymptotic expansion of the integral with respect to the oscillation frequency and to combine this with a Filon-type method. The second method is a variation of a Clenshaw-Curtis rule based on an appropriately chosen weight function that takes into account both the original Jacobi weight and the oscillatory behaviour of the integrand. However, instead of the commonly used simple nodes at the end points of the interval of integration, the authors allow multiple weights.

MSC:
65D32Quadrature and cubature formulas (numerical methods)
41A55Approximate quadratures
65T50Discrete and fast Fourier transforms (numerical methods)
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References:
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