Nyström Methods

Referencias bibliográficas

• Calvo, M.P., Sanz-Serna, J.M.: Order conditions for canonical Runge-Kutta-Nyström methods. BIT 32, 131–142 (1992)
• Calvo, M.P., Sanz-Serna, J.M.: The development of variable-step symplectic integrators, with application to the two-body problem. SIAM J. Sci. Comput. 14, 936–952 (1993)
• Dormand, J.R., El-Mikkawy, M.E.A., Prince, P.J.: Families of Runge-Kutta-Nyström formulae. IMA J. Numer. Anal. 7, 235–250 (1987)
• Dormand, J.R., El-Mikkawy, M.E.A., Prince, P.J.: High-order embedded Runge-Kutta-Nyström formulae. IMA J. Numer. Anal. 7, 423–430 (1987)
• Dormand, J.R., Prince, P.J.: Runge-Kutta-Nyström triples. Comput. Math. Appl. 13(12), 937–949 (1987)
• Hairer, E., Nörsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I. Nonstiff Problems. Springer, Berlin (1993)
• Nyström, E.J.: Ueber die numerische integration von Differentialgleichungen. Acta Soc. Sci. Fenn. 50(13), 1–54 (1925)
• Sanz-Serna, J.M., Calvo, M.P.: Numerical Hamiltonian Problems. Chapman & Hall, London
• Sharp, P.W., Fine, J.M., Burrage, K.: Two-stage and three-stage diagonally implicit Runge-Kutta-Nyström methods of orders three and four. IMA J. Numer. Anal. 10(4), 489–504 (1990)
• Suris, Y.B.: Canonical transformations generated by methods of Runge-Kutta type for the numerical integration of the system $$x^{\prime\prime} = -\partial U/\partial x$$. Zh. Vychisl. Mat. i Mat. Fiz. 29, 202–211 (1987) (in Russian)
• van der Houwen, P.J., Sommeijer, B.P.: Diagonally implicit Runge-Kutta-Nyström methods for oscillatory problems. SIAM J. Numer. Anal. 26(2), 414–429 (1989)
• van der Houwen, P.J., Sommeijer, B.P., Nguyen huu Cong: Stability of collocation-based Runge-Kutta-Nyström methods. BIT 31, 469–481 (1991)