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 -

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$.