Error analysis of the extended Filon-type method for highly oscillatory integrals
نویسندگان
چکیده
منابع مشابه
Error analysis of the extended Filon-type method for highly oscillatory integrals
We investigate the impact of adding inner nodes for a Filon-type method for highly oscillatory quadrature. The error of Filon-type method is composed of asymptotic and interpolation errors, and the interplay between the two varies for different frequencies. We are particularly concerned with two strategies for the choice of inner nodes: Clenshaw–Curtis points and zeros of an appropriate Jacobi ...
متن کاملStability and error estimates for Filon-Clenshaw-Curtis rules for highly-oscillatory integrals
In this paper we obtain new results on Filon-type methods for computing oscillatory integrals of the form ∫ 1 −1 f(s) exp(iks) ds. We use a Filon approach based on interpolating f at the classical Clenshaw-Curtis points cos(jπ/N), j = 0, . . . , N . The rule may be implemented in O(N logN) operations. We prove error estimates which show explicitly how the error depends both on the parameters k ...
متن کاملA combined Filon/asymptotic quadrature method for highly oscillatory problems
A cross between the asymptotic expansion of an oscillatory integral and the Filon-type methods is obtained by applying a Filon-type method on the error term in the asymptotic expansion, which is in itself an oscillatory integral. The efficiency of the approach is investigated through analysis and numerical experiments, and a potential for better methods than current ones is revealed. In particu...
متن کاملFilon-Clenshaw-Curtis rules for a class of highly-oscillatory integrals with logarithmic singularities
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of N , the number of nodes, k the rate of oscillations and a Sobolev-like regularity of the function. We prove that the method is not only robust but the error even decreases, for fixed N , as ...
متن کاملA generalization of Filon-Clenshaw-Curtis quadrature for highly oscillatory integrals
The Filon–Clenshaw–Curtis method (FCC) for the computation of highly oscillatory integrals has been proposed by Domı́nguez, Graham and Smyshlayev and is known to attain surprisingly high precision. Yet, for large values of frequency ω it is not competitive with other versions of the Filon method, which use high derivatives at critical points and exhibit high asymptotic order. In this paper we pr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Research in the Mathematical Sciences
سال: 2017
ISSN: 2197-9847
DOI: 10.1186/s40687-017-0110-4