Integration of Highly Oscillatory Functions

The paper demonstrates approximate methods of integral calculation of highly oscillatory functions. The paper describes a quadrature method which adopts Chebyshev differential matrix to solve the ordinary differential equation (ODE) and thus obtain integral values. This method make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore, even if the system of linear equations is ill-conditioned, regularization method can be adopted to solve it properly and eventually obtain accurate integral results.

oscillatory integrals, Filon method, Levin method, Chebyshev differential matrix, ill-conditioned matrix, Bessel functions