Quadrature rule of interpolatory type for Cauchy integrals

Journal of Computational and Applied Mathematics

Volumn 126, Issue 1-2, 2000, Pages 207-220

  Kim, Philsu ^a   Choi, U Jin ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL GEOMETRY; ERROR ANALYSIS; INTERPOLATION; THEOREM PROVING;

CAUCHY INTEGRALS; QUADRATURE RULE; TRIGONOMETRIC INTERPOLATION;

INTEGRAL EQUATIONS;

EID: 0034497215     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00354-4     Document Type: Article

References (18)

1. M.M. Chawla, N. Jayarajan, Quadrature formulas for cauchy principal value integrals, Computing 15 (1975) 347-355.
2. M.M. Chawla, S. Kumar, Convergence of quadratures for cauchy principal value integrals, Computing 23 (1979) 67-72.
3. C.W. Clenshaw, A.R. Curtis, A method for numerical integration on an automatic computer, Numer. Math. 2 (1960) 197-205.
4. C. Dagnino, E. Santi, On the convergence of spline product quadratures for cauchy principal value integrals, J. Comput. Appl. Math. 36 (1991) 181-187.
5. D. Elliott, Truncation errors in two Chebyshev series approximations, Math. Comp. 19 (1965) 234-248.
6. W.H. Press et al., Numerical Recipes in C, 2nd Edition, Cambridge University press, Cambridge, 1992.
7. R.D. Kurtz et al., The numerical solution of cauchy singular integral equations with application to fracture, Internal J. Fracture 66 (1994) 139-154.
8. A. Gerasoulis, Piecewise-polynomial quadratures for cauchy singular integrals, SIAM J. Numer. Anal. 23 (1986) 891-902.
9. T. Hasegawa, T. Torii, I. Ninomiya, Generalized Chebyshev interpolation and its application to automatic quadrature, Math. Compt. 41 (1983) 537-543.
10. T. Hasegawa, T. Torii, H. Sugiura, An algorithm based on the FFT for a generalized Chebyshev interpolation, Math. Comp. 54 (1990) 195-210.
11. T. Hasegawa, T. Torii, An automatic quadrature for cauchy principal value integrals, Math. Comp. 56 (1991) 741-754.
12. T. Hasegawa, T. Torii, Hilbert and Hadamard transforms by generalized Chebyshev expansion, J. Comput. Appl. Math. 51 (1994) 71-83.
13. N.I. Ioakimidis, A new interpretation of cauchy type singular integrals with an application to singular integral equations, J. Comput. Appl. Math. 14 (1986) 271-278.
14. P. Kim, S. Lee, A piecewise linear quadrature of cauchy singular integrals, J. Comput. Appl. Math. 95 (1998) 101-115.
15. S. Kumar, A note on quadrature formulae for cauchy principal value integrals, J. Inst. Math. Appl. 26 (1980) 447-451.
16. A.P. Orsi, Spline approximation for cauchy principal value integrals, J. Comput. Appl. Math. 30 (1990) 191-201.
17. F.A. Potra, E. Venturino, Low-order methods for cauchy principal value integrals with endpoint singularities, IMA Numer. Anal. 14 (1994) 295-310.
18. P. Rabinowitz, Numerical integration based on approximating spline, J. Comput. Appl. Math. 33 (1990) 73-83.