TY - JOUR
T1 - On Quadrature of Highly Oscillatory Functions
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 - <p style="text-align: justify;">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 $g&#39;(x)\not=0$ 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$.</p>