Diagonally implicit Runge-Kutta-Nystro¨m methods for oscillatory problems
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
On the numerical integration of orbital problems with high order Runge-Kutta-Nyström methods
Applied Numerical Mathematics
Long-Time Energy Conservation of Numerical Methods for Oscillatory Differential Equations
SIAM Journal on Numerical Analysis
New methods for oscillatory problems based on classical codes
Applied Numerical Mathematics
A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators
Journal of Computational and Applied Mathematics
On Magnus Integrators for Time-Dependent Schrödinger Equations
SIAM Journal on Numerical Analysis
Scheifele two-step methods for perturbed oscillators
Journal of Computational and Applied Mathematics
Efficient energy-preserving integrators for oscillatory Hamiltonian systems
Journal of Computational Physics
Special extended Nyström tree theory for ERKN methods
Journal of Computational and Applied Mathematics
Error analysis of explicit TSERKN methods for highly oscillatory systems
Numerical Algorithms
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A one-parameter family of explicit fourth-order methods for oscillatory systems of the form y" + Ky = f (t, y), K being a symmetric positive semi-definite matrix, is obtained. The new methods possess eighth order for the unperturbed problem (f(t,y) ≡ 0), and the free parameter is chosen so that the dispersion or the dissipation are optimized. The stability and phase properties of the new methods are analyzed, obtaining generalized stability regions for the second-order homogeneous linear test model. The numerical experiments carried out show that the new methods are very competitive when they are compared with standard, symplectic and special codes proposed in the scientific literature.