A new theoretical approach to Runge-Kutta methods
SIAM Journal on Numerical Analysis
High-order P-stable multistep methods
Journal of Computational and Applied Mathematics
A symplectic integration algorithm for separable Hamiltonian functions
Journal of Computational Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
High-order symplectic Runge-Kutta-Nystro¨m methods
SIAM Journal on Scientific Computing
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
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
Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?
Journal of Computational and Applied Mathematics
Exponentially fitted explicit Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
Mathematical and Computer Modelling: An International Journal
Structure-Preserving Algorithms for Oscillatory Differential Equations
Structure-Preserving Algorithms for Oscillatory Differential Equations
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The construction of symmetric and symplectic exponentially fitted modified Runge-Kutta-Nystrom (SSEFRKN) methods is considered. Based on the symmetry, symplecticity, and exponentially fitted conditions, new explicit modified RKN integrators with FSAL property are obtained. The new integrators integrate exactly differential systems whose solutions can be expressed as linear combinations of functions from the set {exp(+/-i@wt)}, @w0, i^2=-1, or equivalently from the set {cos(@wt), sin(@wt)}. The phase properties of the new integrators are examined and their periodicity regions are obtained. Numerical experiments are accompanied to show the high efficiency and competence of the new SSEFRKN methods compared with some highly efficient nonsymmetric symplecti EFRKN methods in the literature.