Indefinite integration of oscillatory functions by the Chebyshev series expansion

摘要

An automatic quadrature scheme is presented for evaluating the indefinite integral of oscillatory function ∫x0ƒ(t)eiωtdt, 0⩽x⩽1, of a given function ƒ(t), which is usually assumed to be smooth. The function ƒ(t) is expanded in the Chebyshev series to make an efficient evaluation of the indefinite integral. Combining the automatic quadrature method obtained and Sidi's extrapolation method makes an effective quadrature scheme for oscillatory infinite integral ∫∞aƒ(x) cos ωxdx for which numerical examples are also presented.