Difference schemes for Hamiltonian formalism and symplectic geometry
Journal of Computational Mathematics
SIAM Journal on Numerical Analysis
USSR Computational Mathematics and Mathematical Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
Exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Practical symplectic partitioned Runge--Kutta and Runge--Kutta--Nyström methods
Journal of Computational and Applied Mathematics
Exponentially fitted explicit Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
New methods for oscillatory systems based on ARKN methods
Applied Numerical Mathematics
Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
Mathematical and Computer Modelling: An International Journal
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The aim of this paper is to develop a unified special extended Nystrom tree (SEN-tree) theory which provides a theoretical framework for the order conditions of multidimensional extended Runge-Kutta-Nystrom (ERKN) methods proposed by X. Wu et al. (Wu et al., 2010). The new SEN tree theory is complete and consistent, which has overcome the drawback of the bi-coloured tree theory in H. Yang et al.'s work (Yang et al., 2009) where two ''branch sets'' have to be constructed for the true solutions and for the numerical solutions, respectively.