Runge-Kutta-Nystrom Method with FSAL Property

3 Runge-Kutta-Nystrom Method with FSAL Property. - We give the following definition. 

Definition 2. A Runge-Kutta-Nystrbm method is said to have the FSAL 

For the Runge-Kutta-Nystrom method described by equations (13)-(17), Aguiar, Simos and Tocino have produced the corresponding method that has the FSAL property. This method is given by  

For w 0, the above method is equivalent to the classical symlpectic second algebraic order Runge-Kutta-Nystrom method mentioned in the paper of Calvo and Sanz-Serna.  

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In 52 the author develops a symplectic exponentially fitted modified Runge-Kutta-Nystrom method. The method of development was based on the development of symplectic exponentially fitted modified Runge-Kutta-Ny-strom method by Simos and Vigo-Aguiar. The new method is a two-stage second-order method with FSAL-property (first step as last). 

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