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An adaptive splitting algorithm was implemented for numerical evaluation of Fourier-type highly oscillatory integrals involving stationary point. Accordingly, a modified Levin collocation method was coupled with multi-resolution quadratures in order to tackle the stationary point and irregular oscillations of the integrand caused by    ω   . Some test problems are included to verify the accuracy of the proposed methods.

Fast Computation of Integrals with Fourier-Type Oscillator Involving Stationary Point