On generalized quadrature rules for fast oscillatory integrals

Abstract In this paper, we present numerical analysis for the generalized quadrature rule for ∫ a b f ( x ) w ( r , x ) d x , where w ( r , x ) is an oscillatory function, and derive higher order generalized quadrature rules. The results show that the generalized quadrature rules are efficient for Bessel-trigonometric transformations and the accuracy increases when oscillation becomes faster.

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