id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
cord-027118-2xm8nkmi	Sevastianov, Leonid A.	An Effective Stable Numerical Method for Integrating Highly Oscillating Functions with a Linear Phase	2020-06-15		.txt	text/plain	3679	209	53	An approach based on the fruitful idea of Levin, which allows the use of the collocation method to approximate the slowly oscillating part of the antiderivative of the desired integral, allows reducing the calculation of the integral of a rapidly oscillating function (with a linear phase) to solving a system of linear algebraic equations with a triangular or Hermitian matrix. In particular, the use in specific implementations of the Levin collocation method in the physical space of degenerate Chebyshev differentiation matrices, which also have eigenvalues differing by orders of magnitude, makes it impossible to construct a stable numerical algorithm for solving the resulting SLAEs. The approach to solving the differential equation of the Levin method, described in [5, 6, 8] , is based on the approximation of the solution, as well as the integrand phase and amplitude functions in the form of expansion into finite series in Chebyshev polynomials.	./cache/cord-027118-2xm8nkmi.txt	./txt/cord-027118-2xm8nkmi.txt