Geodesic
Indefinite integration of oscillatory functions
Applicationes Mathematicae, Tome 25 (1999) no. 3, pp. 301-311 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function $\int_x^yi f(t) e^{iωt} dt$, -1 ≤ x y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.
DOI : 10.4064/am-25-3-301-311
Keywords: indefinite integration, second-order linear difference equation, oscillatory function

Paweł Keller 1

1 
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Paweł Keller. Indefinite integration of oscillatory functions. Applicationes Mathematicae, Tome 25 (1999) no. 3, pp. 301-311. doi: 10.4064/am-25-3-301-311

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