A universal solution to one-dimensional oscillatory integrals

How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave’s propagation and scattering. Levin method is a classical quadrature method for this type of integrals. Unfortunately it is susceptible to the system of linear equations’ ill-conditioned behavior. We bring forward a universal quadrature method in this paper,which adopts Chebyshev differ-ential matrix to solve the ordinary differential equation (ODE). This method can not only obtain the indefinite integral’ function values directly,but also make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore,even if the system of linear equations in our method is ill-conditioned,TSVD method can be adopted to solve them properly and eventually obtain accurate integral re-sults,thus making a breakthrough in Levin method’s susceptivity to the system of linear equations’ill-conditioned behavior.