References
- V.A. Avdyushev, Special perturbation theory methods in celestial mechanics. I. Principles for the construction and substantiation of the application, Russ. Phys. J. 49 (2006), pp. 1344–1353. doi: 10.1007/s11182-006-0264-9
- J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Springer, New York, 1989.
- J.C. Butcher, Numerical Methods for Ordinary Differential Equations, 2nd ed., Wiley, Chichester, 2008.
- J.P. Coleman, Order conditions for a class of two-step methods for y″=f(x,y), IMA J. Numer. Anal. 23 (2003), pp. 197–220. doi: 10.1093/imanum/23.2.197
- R. D'Ambrosio, E. Esposito, and B. Paternoster, General linear methods for y″=f(y(t)), Numer. Algorithms 61 (2012), pp. 331–349. doi: 10.1007/s11075-012-9637-z
- R. D'Ambrosio, G. De Martino, and B. Paternoster, Order conditions for general linear Nyström methods, Numer. Algorithms 65 (2014), pp. 579–595. doi: 10.1007/s11075-013-9819-3
- J.M. Franco, Runge-Kutta-Nyström methods adapted to the numerical integration of perturbed oscillators, Comput. Phys. Comm. 147 (2002), pp. 770–787. doi: 10.1016/S0010-4655(02)00460-5
- E. Hairer, S.P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed., Springer-Verlag, Berlin, 2002.
- J. Li, S. Deng, and X. Wang, Multi-step Nyström methods for general second-order initial value problems y″(t)=f(t,y(t),y′(t)), Int. J. Comput. Math. doi:10.1080/00207160.2018.1464154.
- J.I. Ramos and C.M. García-López, Piecewise-linearized methods for initial-value problems, Appl. Math. Comput. 82 (1997), pp. 459–467.
- H. Ramos, G. Singh, V. Kanwar, and S. Bhatia, An efficient variable step-size rational Falkner-type method for solving the special second-order IVP, Appl. Math. Comput. 291 (2016), pp. 39–51.
- A. Sesappa Rai and U. Ananthakrishnaiah, Obrechkoff methods having additional parameters for general second-order differential equations, J. Comput. Appl. Math. 79 (1997), pp. 167–182. doi: 10.1016/S0377-0427(96)00132-X
- J. Vigo-Aguiar and H. Ramos, Variable stepsize implementation of multistep methods for y″=f(x,y), J. Comput. Appl. Math. 192 (2006), pp. 114–131. doi: 10.1016/j.cam.2005.04.043
- X. Wu, X. You, W. Shi, and B. Wang, ERKN integrators for systems of oscillatory second-order differential equations, Comput. Phys. Comm. 181 (2010), pp. 1873–1887. doi: 10.1016/j.cpc.2010.07.046
- X. You, J. Zhao, H. Yang, Y. Fang, and X. Wu, Order conditions for RKN methods solving general second-order oscillatory systems, Numer. Algorithms 66 (2014), pp. 147–176. doi: 10.1007/s11075-013-9728-5