Browsing by Author "Kayijuka I."

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    FAST APPROXIMATION OF ALGEBRAIC AND LOGARITHMIC HYPERSINGULAR TYPE SINGULAR INTEGRALS WITH HIGHLY OSCILLATORY KERNEL
    (Etamaths Publishing, 2020) Kayijuka I.; Ege S.M.; Konuralp A.; Topal F.S.
    Herein, highly oscillatory integrals with hypersingular type singularities are studied. After transforming the original integral into a sum of line integrals over a positive semi-infinite interval, a Gauss-related quadrature rule is constructed. The vehicle utilized is the moment's information. The comparison of two algorithms (Chebyshev and its modified one) to produce the recursion coefficients that satisfy orthogonal polynomial with respect to Gautschi logarithmic weight function, is investigated. Lastly, numerical examples are given to substantiate the effectiveness of the proposed method. © 2020, Etamaths Publishing. All rights reserved.
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    Fast gauss-related quadrature for highly oscillatory integrals with logarithm and cauchy-logarithmic type singularities
    (University of Alberta, 2021) Kayijuka I.; Ege S.M.; Konuralp A.; Topal F.S.
    This paper presents an efficient method for the computation of two highly oscillatory integrals having logarithmic and Cauchy-logarithmic singularities. This approach first requires the transformation of the original oscillatory integrals into a sum of line integrals with semi-infinite intervals. Afterwards, the coefficients of the three-term recurrence relation that satisfy the orthogonal polynomial are obtained by using the method based on moments, where classical Laguerre and Gautschi’s logarithmic weight functions are employed. The algorithm reveals that with fixed n, the method is capable of achieving significant figures within a short time. Furthermore, the approach yields higher accuracy as the frequency increases. The results of numerical experiments are given to substantiate our theoretical analysis. © 2021 Institute for Scientific Computing and Information.
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    Clenshaw–Curtis algorithms for an efficient numerical approximation of singular and highly oscillatory Fourier transform integrals
    (Elsevier B.V., 2021) Kayijuka I.; Ege Ş.M.; Konuralp A.; Topal F.S.
    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® 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. © 2020 Elsevier B.V.
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    AN EFFICIENT ALGORITHM FOR EVALUATION OF OSCILLATORY INTEGRALS HAVING CAUCHY AND JACOBI TYPE SINGULARITY KERNELS
    (Korean Society for Computational and Applied Mathematics, 2022) Kayijuka I.; Ege Ş.M.; Konuralp A.; Topal F.S.
    Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Cheby-shev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical ex-amples are given in support of our theoretical analysis. © 2022 KSCAM.