Numerical calculation of integrals with strongly oscillating integrand

Authors:
A. I. van de Vooren and H. J. van Linde

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

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a method is presented for evaluating

The idea is to approximate 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 . An expression for the remainder term is also included. Results for the real part are exact if is of at most 7th degree and for the imaginary part if is of at most 8th degree.

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DOI:
https://doi.org/10.1090/S0025-5718-1966-0192644-8

Article copyright:
© Copyright 1966
American Mathematical Society