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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical indefinite integration by double exponential sinc method


Authors: Ken'ichiro Tanaka, Masaaki Sugihara and Kazuo Murota
Journal: Math. Comp. 74 (2005), 655-679
MSC (2000): Primary 41A30, 41A25, 65D30
Published electronically: November 2, 2004
MathSciNet review: 2114642
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Abstract: We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with $N$ integrand function evaluations is

\begin{displaymath}\mathrm{O}(\exp(-c_1 N/\log(c_2 N))) \end{displaymath}

for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary sinc method. Computational results show the accordance of the actual convergence rates with the theoretical estimate.


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Additional Information

Ken'ichiro Tanaka
Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Email: kenitiro@misojiro.t.u-tokyo.ac.jp

Masaaki Sugihara
Affiliation: Department of Computational Science and Engineering, School of Engineering, Nagoya University, Nagoya 464-8603, Japan
Email: sugihara@na.cse.nagoya-u.ac.jp

Kazuo Murota
Affiliation: Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
Email: murota@mist.i.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01724-7
PII: S 0025-5718(04)01724-7
Keywords: Numerical indefinite integration, double exponential transformation, sinc numerical method
Received by editor(s): May 9, 2003
Published electronically: November 2, 2004
Additional Notes: This work is supported by the 21st Century COE Program on Information Science and Technology Strategic Core and a Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan
Article copyright: © Copyright 2004 American Mathematical Society