Geodesic
Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 53-69.

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For initial value problem (IVPs) in ordinary second order differential equations of the special form $y^{\prime \prime }=f\left(x,y\right)$ possessing oscillating solutions, diagonally implicit Runge–Kutta–Nystrom (DIRKN) formula-pairs of orders 5(4) in 5-stages are derived in this paper. The method is zero dissipative, thus it possesses a non-empty interval of periodicity. Some numerical results are presented to show the applicability of the new method compared with existing Runge–Kutta (RK) method applied to the problem reduced to first-order system.
Classification : 65L05
Keywords: Initial value problems; Runge–Kutta–Nystrom pairs; zero dissipative 
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     title = {Zero {Dissipative} {DIRKN} {Pairs} of {Order} 5(4) for {Solving} {Special} {Second} {Order} {IVPs}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Imoni, S. O.; Ikhile, M. N. O. Zero Dissipative DIRKN Pairs of Order 5(4) for Solving Special Second Order IVPs. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 53-69. http://geodesic.mathdoc.fr/item/AUPO_2014__53_2_a3/