Diagonally implicit Runge-Kutta-Nystro¨m methods for oscillatory problems
SIAM Journal on Numerical Analysis
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Computation of the interval of stability of Runge-Kutta-Nystro¨m methods
Journal of Symbolic Computation
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
A conditionally P-stable fourth-order exponential-fitting method for y'' = f(f, y)
Journal of Computational and Applied Mathematics
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
A phase-fitted collocation-based Runge-Kutta-Nyström method
Applied Numerical Mathematics
Stability analysis of frequency and step length dependent Runge-Kutta-Nyström methods
Future Generation Computer Systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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We analyze the linear stability properties of mixed collocation Runge-Kutta-Nystrom (RKN) methods for the second order Ordinary Differential Equations y^''=f(x,y). In particular we consider the influence of the collocation nodes on the stability region, analyzing in detail the case of frequency and step length dependent RKN methods obtained through mixed collocation which are based on Gauss, Radau and Lobatto nodes.