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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:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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