Numerical calculation of integrals with strongly oscillating integrand
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- by A. I. van de Vooren and H. J. van Linde PDF
- Math. Comp. 20 (1966), 232-245 Request permission
Abstract:
In this paper a method is presented for evaluating \[ \int _0^N {f(x){e^{iwx}}} dx{\text { where }}\omega N = p \cdot 2\pi ,{\text { }}p{\text { integer}}{\text {.}}\] The idea is to approximate $f(x)$ instead of the whole integrand by aid of polynomials. The Romberg-Stiefel algorithm has been extended to this case. The new method is complementary to the usual Romberg-Stiefel algorithm in the sense that it is more advantageous for larger values of $\omega$. An expression for the remainder term is also included. Results for the real part are exact if $f(x)$ is of at most 7th degree and for the imaginary part if $f(x)$ is of at most 8th degree.References
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Additional Information
- © Copyright 1966 American Mathematical Society
- Journal: Math. Comp. 20 (1966), 232-245
- MSC: Primary 65.55; Secondary 65.25
- DOI: https://doi.org/10.1090/S0025-5718-1966-0192644-8
- MathSciNet review: 0192644