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International Journal of Computer Mathematics Volume 28, 1989 - Issue 1-4
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Original Articles

Scaled runge-kutta-nyström methods for the second order differential equation ÿ = f(x,y)

G. Papageorgiou Department of Mathematics, National Technical University of Athens, Athens, Greece
&
Ch. Tsitouras Department of Mathematics, National Technical University of Athens, Athens, Greece
Pages 139-150 | Received 13 Oct 1987, Published online: 19 Mar 2007

Citations (13)

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Ch. Tsitouras & G. Papageorgiou. (1993) Interpolating runge-kutta-nyström methods of high order. International Journal of Computer Mathematics 47:3-4, pages 209-217.
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Articles from other publishers (12)

I. Th. Famelis, S. Tsitmidelis & Ch. Tsitouras. Evolutionary generation of high order Runge – Kutta – Nyström type pairs for solving y(4) = f (x,y). Evolutionary generation of high order Runge – Kutta – Nyström type pairs for solving y(4) = f (x,y).
S. N. Papakostas, S. Tsitmidelis & Ch. Tsitouras. Evolutionary generation of 7th order Runge – Kutta – Nyström type methods for solving y(4) = f(x,y). Evolutionary generation of 7th order Runge – Kutta – Nyström type methods for solving y(4) = f(x,y).
Zhang Xiao-Yong & Li Yan. (2012) Generalized Laguerre pseudospectral method based Laguerre interpolation. Applied Mathematics and Computation 219:5, pages 2545-2563.
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Ben-yu Guo & Jian-ping Yan. (2009) Legendre–Gauss collocation method for initial value problems of second order ordinary differential equations. Applied Numerical Mathematics 59:6, pages 1386-1408.
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Abdul Hadi Alim A. Khader. (2008) Error Control Policy for Initial Value Problems with Discontinuities and Delays. Kyungpook mathematical journal 48:4, pages 665-684.
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Moawwad El-Mikkawy & El-Desouky Rahmo. (2003) A new optimized non-FSAL embedded Runge–Kutta–Nystrom algorithm of orders 6 and 4 in six stages. Applied Mathematics and Computation 145:1, pages 33-43.
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G. Papageorgiou & I.Th. Famelis. (2001) Continuous Runge-Kutta-Nyström methods for initial value problems with periodic solutions. Computers & Mathematics with Applications 42:8-9, pages 1165-1176.
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S. N. Papakostas & Ch. Tsitouras. (1997) Highly Continuous Interpolants for One-Step ODE Solvers and their Application to Runge--Kutta Methods. SIAM Journal on Numerical Analysis 34:1, pages 22-47.
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Arne Marthinsen. (1996) Continuous extensions to Nyström methods for second order initial value problems. BIT Numerical Mathematics 36:2, pages 309-332.
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G. Papageorgiou & Ch. Tsitouras. (1996) Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors. Journal of Computational and Applied Mathematics 69:1, pages 1-11.
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Ch. Tsitouras, G. Papageorgiou & T. Kalvouridis. (1992) On the efficiency of Runge-Kutta-Nystrom methods with interpolants for solving equations of the form Y? = F(T, Y, Y?) over short timespans. Celestial Mechanics and Dynamical Astronomy 53:4, pages 329-346.
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Ch. Tsitouras & G. Papageorgiou. (1990) Runge-Kutta interpolants based on values from two successive integration stepsRunge-Kutta Interpolanten gestützt auf Werte von zwei sukzessiven Integrationsschritten. Computing 43:3, pages 255-266.
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