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Trigonometrically fitted predictor–corrector methods for IVPs with oscillating solutions. (English) Zbl 1027.65095

Summary: 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.

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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