A new Sixth-Order Runge - Kutta - Nystro ̈m Method for Special Second Order Ordinary Differential Equations
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Initial value problems, ODE, One step, Order Conditions, Runge-Kutta-Nystro ̈m methods, Special Second-order
Abstract
this article, an explicit Runge-Kutta-Nystr m method of sixth order for solving directly second-order ordinary differential equations is constructed. The stability property of the new method is discussed. Numerical illustrations are presented to show the efficiency of the new method by comparing it with other existing Runge-Kutta-Nystr m and Runge-Kutta methods in the scientific literature.
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