Indefinite integration of oscillatory functions
Tom 25 / 1998
Applicationes Mathematicae 25 (1998), 301-311
DOI: 10.4064/am-25-3-301-311
Streszczenie
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.
