Trigonometrically fitted predictor–corrector methods for IVPs with oscillating solutions

In this paper we develop a trigonometrically fitted predictor–corrector (P–C) scheme, which is based on the well-known two-step second-order Adams–Bashforth method (as predictor) and on the third-order Adams–Moulton method (as corrector). Numerical experiments show that the new trigonometrically fitted P–C method is substantially more efficient than widely used methods for the numerical solution of initial-value problems (IVPs) with oscillating solutions.