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Indefinite integration of oscillatory functions. (English) Zbl 0998.65034

Summary: A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function \(\int^y_x f(t)e^{i\omega t} dt\), \(-1\leq x < y \leq 1\), \(\omega\neq 0\), 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.

MSC:

65D30 Numerical integration
65Q05 Numerical methods for functional equations (MSC2000)
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
65T40 Numerical methods for trigonometric approximation and interpolation
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