Uniform approximations to Cauchy principal value integrals of oscillatory functions

Applied Mathematics and Computation

Volumn 215, Issue 5, 2009, Pages 1886-1894

  Wang, Haiyong ^a   Xiang, Shuhuang ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Cauchy principal value; Clenshaw Curtis method; Oscillatory integral; Stability

Indexed keywords

CAUCHY INTEGRAL; CAUCHY PRINCIPAL VALUE; CHEBYSHEV POINTS; CLENSHAW-CURTIS METHOD; INTEGRATION RULE; INTERPOLATORY; NUMERICAL EVALUATIONS; NUMERICAL EXPERIMENTS; OSCILLATORY FUNCTIONS; OSCILLATORY INTEGRAL; OSCILLATORY INTEGRANDS; SMOOTH FUNCTIONS; UNIFORM APPROXIMATION;

FAST FOURIER TRANSFORMS;

INTEGRATION;

EID: 70349866668     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.07.041     Document Type: Article

References (14)

1. Abramowitz M., and Stegun I.A. Handbook of Mathematical Functions (1964), National Bureau of Standards, Washington, DC
2. Capobianco M.R., and Criscuolo G. On quadrature for Cauchy principal value integrals of oscillatory functions. J. Comput. Appl. Math. 156 (2003) 471-486
3. Cash J.R. A note on the numerical solution of linear recurrence relations. Numer. Math. 34 (1980) 371-386
4. Davis P.J., and Rabinowitz P. Methods of Numerical Integration. Second ed. (1984), Academic Press
5. Clenshaw C.W., and Curtis A.R. A method for numerical integration on an automatic computer. Numer. Math. 2 (1960) 197-205
6. Elliott D. Truncation errors in two Chebyshev series approximations. Math. Comp. 19 (1965) 234-248
7. Evans G.A., and Webster J.R. A comparison of some methods for the evaluation of highly oscillatory integrals. J. Comput. Appl. Math. 112 (1999) 55-69
8. Gentleman W.M. Implementing Clenshaw-Curtis quadrature Π: computing the cosine transformation. Commun. ACM 15 (1972) 343-346
9. Gradshteyn I.S., and Ryzhik I.M. Tables of Integrals, Series, and Products. sixth ed. (2000), Academic Press, San Diego, CA
10. Hasegawa T. Uniform approximations to finite Hilbert transform and its dervatives. J. Comput. Appl. Math. 163 (2004) 127-138
11. Hasegawa T., and Torii T. An automatic quadrature for Cauchy principal value integrals. Math. Comput. 56 (1991) 741-754
12. Okecha G.E. Quadrature formulae for Cauchy principal value integrals of oscillatory kind. Math. Comput. 49 (1987) 259-268
13. Okecha G.E. Hermite interpolation and a method for evaluating Cauchy principal value integrals of oscillatory kind. Kragujevac J. Math. 29 (2006) 91-98
14. Piessens R., and Poleunis F. A numerical method for the integration of oscillatory functions. BIT 11 (1971) 317-327