Abstract
The paper presents a trigonometrically-fitted implicit third derivative Runge-Kutta-Nystöm method (TTRKNM) whose coefficients depend on the frequency and stepsize for periodic initial value problems. The TTRKNM is a pair of methods which is obtained from its continuous version and applied to produce simultaneous approximations to the solution and its first derivative at each point in the interval of interest. A discussion of the stability property of the method is given. Numerical experiments are performed to demonstrate the accuracy and efficiency of the method.
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Jator, S.N. Implicit third derivative Runge-Kutta-Nyström method with trigonometric coefficients. Numer Algor 70, 133–150 (2015). https://doi.org/10.1007/s11075-014-9938-5
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DOI: https://doi.org/10.1007/s11075-014-9938-5