1 |
R. Piessens and M. Branders, The evaluation and application of some modified moments, BIT, 13 (1973) 443-450.
DOI
|
2 |
H. Kang, S. Xiang, and G. He, Computation of integrals with oscillatory and singular integrands using Chebyshev expansions, J. Comput. Appl. Math. 242 (2013), 141-156.
DOI
|
3 |
R. Chen, Fast computation of a class of highly oscillatory integrals, Appl. Math. Comput. 227 (2014), 494-501.
DOI
|
4 |
I. Kayijuka, J.P. Ndabakuranye, and A.I. Hascelik, Computational efficiency of singular and oscillatory integrals with algebraic singularities, Asian J. Math. Comput. Res. 25 (2018), 285-302.
|
5 |
H. Wang and S. Xiang, Uniform approximations to Cauchy principal value integrals of oscillatory functions, Appl. Math. Comput. 215 (2009), 1886-1894.
DOI
|
6 |
P.K. Kythe and M.R. Schaferkotter, Handbook of computational method for integration, Chapman & Hall/CRC, ISBN-13: 978-1584884286, New York, 2004.
|
7 |
S. Lu, A Class of Oscillatory Singular Integrals Boundedness, Int. J. Appl. Math. Sci. 2 (2005), 47-64.
|
8 |
W. Sun and N.G. Zamani, Adaptive mesh redistribution for the boundary element in elastostatics, Comput. Struct. 36 (1990), 1081-1088.
DOI
|
9 |
L.N.G. Filon, On a Quadrature Formula for Trigonometric Integrals, Proc. R. Soc. Edinburgh, 1930.
|
10 |
H. Brunner, Open problems in the computational solution of Volterra functional equations with highly oscillatory kernels, Isaac Newt. Institute, HOP 2007, 1-14.
|
11 |
V. Dominguez, Filon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities, J. Comput. Appl. Math. 261 (2014), 299-319.
DOI
|
12 |
M.R. Capobianco and G. Criscuolo, On quadrature for Cauchy principal value integrals of oscillatory functions, 156 (2003), 471-486.
DOI
|
13 |
F.G. RICOMI, On the finite Hilbert transformation, Quarterly J. Math. 2 (1951), 199-211.
DOI
|
14 |
F.B. Hildebrand, Introduction to Numerical Analysis, 2nd Ed., Dover Publication Inc., New york, 2003.
|
15 |
H. Kang and X. Shao, Fast computation of singular oscillatory fourier transforms, Abstr. Appl. Anal. 1 (2014), 1-8.
DOI
|
16 |
S. Olver, Moment-free numerical approximation of highly oscillatory integrals with stationary points, Eur. J. Appl. Math. 18 (2007), 435-447.
DOI
|
17 |
A. Erdelyi, Asymptotic representations of Fourier integrals and the method of stationary phase, J. Soc. Indust. Appl. Math. 3 (1955), 17-27.
DOI
|
18 |
G.B. Arfken, Mathematical Methods For Physicists, Sixth Edit., Elsevier Inc., 2005.
|
19 |
H. Brunner, On the numerical solution of first-kind Volterra integral equations with highly oscillatory kernels, Isaac Newton Institute, HOP 2010.
|
20 |
L.N. Trefethen, Is Gauss quadrature better than Clenshaw-Curtis, SIAM Rev. 50 (2008), 67-87.
DOI
|
21 |
D. Huybrechs and S. Vandewalle, On the evaluation of highly oscillatory integrals by analytic continuation, SIAM J. Numer. Anal. 44 (2006), 1026-1048.
DOI
|
22 |
J.W. Cooley and J.W. Tukey, An Algorithm for the Machine Calculation of Complex Fourier Series, Math. Comput. 19 (1965), 297-301.
DOI
|
23 |
Idrissa Kayijuka, Serife Muge Ege, Ali Konuralp and Fatma Serap Topal, Clenshaw-Curtis algorithms for an efficient numerical approximation of singular and highly oscillatory Fourier transform integrals, J. Comput. App. Math. 385 (2021), no:113201.
|
24 |
J.C. Mason and E. Venturino, Integration Methods of Clenshaw-Curtis Type, Based on Four Kinds of Chebyshev Polynomials, Multivar. Approx. Splines, Birkhause, Bessel, 1996.
|
25 |
C.W. Clenshaw and A.R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960), 197-205.
DOI
|
26 |
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Washington DC, 1964.
|
27 |
P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, second ed., Academic Press, Orland, FL, 1984.
|
28 |
H. Takemitsu and T. Tatsuo, An automatic quadrature for Cauchy Principal Value integrals, Math. Comp. 56 (1994), 741-754.
DOI
|
29 |
M.A. Hamed and B. Cummins, A numerical integration formula for the solution of the singular integral equation for classical crack problems in plane and antiplane elasticity, J. King Saud Un. 3 (1991) 217-230.
|
30 |
J.C. Mason and D.C. Handscomb, Chebyshev Polynomials, A CRC Press Company, 2003.
|
31 |
Idrissa Kayijuka, Suliman Alfaqeih and Turgut Ozis, Application of the Cauchy integral approach to Singular and Highly Oscillatory Integrals, Int. J. Comp. Math. 98 (2021), 2097-2114.
DOI
|
32 |
G. Criscuolo, A new algorithm for Cauchy principal value and Hadmard finit-part integrals, J. Comput. Appl. Math. 78 (1997), 255-275.
DOI
|