On an improved-Levin oscillatory quadrature method

Performance of an improved-Levin quadrature method for oscillatory integrals is studied. In the study, the behavior of the target system of linear equations is analyzed and an error reduction factor is proposed to measure the behaviorʼs impact on the integral result. Numerical investigations show that the error reduction factor is extremely small for ill-conditioned case, and the ill-conditioning has little impact on the final integral result. Therefore, the concerned quadrature method is numerically very stable and it has addressed the Levin methodʼs problem of being susceptible to the ill-conditioning.