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A fourth algebraic order trigonometrically fitted predictor-corrector scheme for IVPs with oscillating solutions. (English) Zbl 1063.65060
Summary: A scheme of trigonometrically fitted predictor-corrector (P-C) Adams-Bashforth-Moulton methods is constructed. 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 test 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 (IVPs) with oscillating solutions.
MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general