@Article{JCM-24-579, author = {}, 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} }