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Volume 24, Issue 5
On Quadrature of Highly Oscillatory Functions

Shu-huang Xiang & Yong-xiong Zhou

J. Comp. Math., 24 (2006), pp. 579-590.

Published online: 2006-10

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  • Abstract

Some quadrature methods for integration of $\int_a^b f(x)e^{i \omega g(x)}dx$ for rapidly oscillatory functions are presented. These methods, based on the lower order remainders of Taylor expansion and followed the thoughts of Stetter [9], Iserles and Nørsett [5], are suitable for all $\omega$ and the decay of the error can be increased arbitrarily in case that $g'(x)\not=0$ for $x\in [a,b]$, and easy to be implemented and extended to the improper integration and the general case $ I[f]=\int_a^b f(x)e^{ig(\omega,x)} dx$.

  • Keywords

Oscillatory integral, quadrature, Filon-type method, Taylor expansion.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-24-579, author = {Shu-huang Xiang and Yong-xiong Zhou}, title = {On Quadrature of Highly Oscillatory Functions}, journal = {Journal of Computational Mathematics}, year = {2006}, volume = {24}, number = {5}, pages = {579--590}, abstract = {

Some quadrature methods for integration of $\int_a^b f(x)e^{i \omega g(x)}dx$ for rapidly oscillatory functions are presented. These methods, based on the lower order remainders of Taylor expansion and followed the thoughts of Stetter [9], Iserles and Nørsett [5], are suitable for all $\omega$ and the decay of the error can be increased arbitrarily in case that $g'(x)\not=0$ for $x\in [a,b]$, and easy to be implemented and extended to the improper integration and the general case $ I[f]=\int_a^b f(x)e^{ig(\omega,x)} dx$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8776.html} }
TY - JOUR T1 - On Quadrature of Highly Oscillatory Functions AU - Shu-huang Xiang & Yong-xiong Zhou JO - Journal of Computational Mathematics VL - 5 SP - 579 EP - 590 PY - 2006 DA - 2006/10 SN - 24 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8776.html KW - Oscillatory integral, quadrature, Filon-type method, Taylor expansion. AB -

Some quadrature methods for integration of $\int_a^b f(x)e^{i \omega g(x)}dx$ for rapidly oscillatory functions are presented. These methods, based on the lower order remainders of Taylor expansion and followed the thoughts of Stetter [9], Iserles and Nørsett [5], are suitable for all $\omega$ and the decay of the error can be increased arbitrarily in case that $g'(x)\not=0$ for $x\in [a,b]$, and easy to be implemented and extended to the improper integration and the general case $ I[f]=\int_a^b f(x)e^{ig(\omega,x)} dx$.

Shu-huang Xiang and Yong-xiong Zhou. (2006). On Quadrature of Highly Oscillatory Functions. Journal of Computational Mathematics. 24 (5). 579-590. doi:
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