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This paper investigates the implementation of Clenshaw-Curtis algorithms on singular and highly oscillatory integrals for efficient evaluation of the finite Fourier-type transform of integrands with endpoint singularities. In these methods, integrands are truncated by orthogonal polynomials and special function series term by term. Then their singularity types are computed using third and fourth-order homogeneous recurrence relations. The first approach reveals its efficiency for low, moderate and very high frequencies, whereas the second one, is more efficient for small values of frequencies. Moreover, all the results were found quite satisfactory. Algorithms and programming code in MATHEMATICA (R) 9.0 are provided for the implementation of methods for automatic computation on a computer. Lastly, illustrative numerical experiments and comparison of the proposed Clenshaw-Curtis algorithms to the steepest descent method are mentioned in support of our theoretical analysis in the examples section. (C) 2020 Elsevier B.V. All rights reserved.

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http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/7186

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