Using modified moments for numerical solution of oscillatory integrals
Numerical methods for strongly oscillatory and singular functions are given in this paper. We present an alternative numerical solution for of oscillatory integrals of the general form
Where and are smooth functions in the interval [a, b]. Also and . In order to achieve this goal and avoid singularity, the mentioned integral is solved by the modified moments using interpolating at the Chebyshev points. Finally, we give some experiments for showing efficiency and validity of the method.
Keywords: Approximation, Highly Oscillatory Integrals, Hermite Interpolation, Orthogonal Polynomials, Moments, Uniform Approximation.
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