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Abstract
In this paper we obtain new results on Filontype methods for computing oscillatory integrals of the form $\int_{1}^1 f(s) \exp({\rm i}ks) \ {\rm d}s $.
We use a Filon approach based on interpolating $f$ at the classical ClenshawCurtis points $\cos(j\pi/N), \ j = 0, \ldots , N$. The rule may be implemented in $\mathcal{O}(N \log N)$ operations. We prove error estimates which show explicitly how the error depends both on the parameters $k$ and $N$ and on the Sobolev regularity of $f$. In particular we identify the regularity of $
f$
required to ensure the maximum rate of decay of the error as $k
\rightarrow \infty$.
We also describe a method for implementating the method and prove its stability both when $N \leq k$ and $N>k$.
Numerical experiments illustrate both the stability of the algorithm and the sharpness of the error estimates.
Original language  English 

Pages (fromto)  12531280 
Number of pages  28 
Journal  IMA Journal of Numerical Analysis 
Volume  31 
Issue number  4 
DOIs  
Publication status  Published  2011 
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 1 Finished

Boundary Integral Equation Methods for HF Scattering Problems
Graham, I. & Smyshlyaev, V. P.
Engineering and Physical Sciences Research Council
24/03/09 → 23/09/12
Project: Research council