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In this work, a third-order four-stage symplectic explicit trigonometrically-fitted Runge–Kutta–Nyström (RKN) method for the numerical integration of second order initial value problems with oscillatory solutions based on Simos technique is constructed. The numerical results obtain signify the accuracy of the proposed method in comparison with other symplectic and non-symplectic RKN methods. AMS Subject Classification: 65L05, 65L06

international journal of pure and applied mathematics

A FOUR-STAGE THIRD-ORDER SYMPLECTIC EXPLICIT TRIGONOMETRICALLY-FITTED RUNGE--KUTTA--NYSTR\"{O}M METHOD FOR THE NUMERICAL INTEGRATION OF OSCILLATORY INITIAL-VALUE PROBLEMS