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Mathematics of Computation

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Fast integration of highly oscillatory integrals with exotic oscillators


Authors: Shuhuang Xiang and Haiyong Wang
Journal: Math. Comp. 79 (2010), 829-844
MSC (2000): Primary 65D32, 65D30
DOI: https://doi.org/10.1090/S0025-5718-09-02279-0
Published electronically: August 26, 2009
MathSciNet review: 2600545
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Abstract: In this paper, we present an efficient Filon-type method for the integration of systems containing Bessel functions with exotic oscillators based on a diffeomorphism transformation and give applications to Airy transforms. Preliminary numerical results show the effectiveness and accuracy of the quadrature for large arguments of integral systems.


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Additional Information

Shuhuang Xiang
Affiliation: Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, People’s Republic of China
Address at time of publication: Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Haiyong Wang
Affiliation: Department of Applied Mathematics and Software, Central South University, Changsha, Hunan 410083, People’s Republic of China

DOI: https://doi.org/10.1090/S0025-5718-09-02279-0
Keywords: Oscillatory integrals, diffeomorphism transformation, Filon-type method.
Received by editor(s): December 28, 2007
Received by editor(s) in revised form: October 25, 2008, and March 18, 2009
Published electronically: August 26, 2009
Additional Notes: This work is supported by NSF of China (No.10771218) and the Program for New Century Excellent Talents in University, State Education Ministry, China.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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