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Numerical Calculation of Integrals with Strongly Oscillating Integrand
| Content Provider | Scilit |
|---|---|
| Author | van de Vooren, A. I. van Linde, H. J. |
| Copyright Year | 1966 |
| Description | 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. |
| Related Links | https://www.ams.org/mcom/1966-20-094/S0025-5718-1966-0192644-8/S0025-5718-1966-0192644-8.pdf |
| Ending Page | 245 |
| Page Count | 14 |
| Starting Page | 232 |
| ISSN | 00255718 |
| e-ISSN | 10886842 |
| DOI | 10.2307/2003503 |
| Journal | Mathematics of Computation |
| Issue Number | 94 |
| Volume Number | 20 |
| Language | English |
| Publisher | Duke University Press |
| Access Restriction | Open |
| Subject Keyword | Artificial Intelligence Integrand Stiefel Romberg Text Iwx Cdot Integer Remainder Polynomials |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Algebra and Number Theory Computational Mathematics |
