A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions

A scheme of trigonometrically fitted predictor-corrector (P-C) Adams-Bashforth-Moulton methods is constructed in this paper. Our new P-C method is based on the third order Adams-Bashforth scheme (as predictor) and on the fourth order Adams-Moulton scheme (as corrector). We tested the efficiency of our newly developed scheme against well known methods, with excellent results. The numerical experimentation showed that our method is considerably more efficient compared to well known methods used for the numerical solution of initial value problems with oscillating solutions.