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
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
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We present a symbolic-numerical package to analyze the linear stability properties of Runge-Kutta-Nystrom methods for y^'^'=f(x,y), which are suitable for ordinary differential equations having periodic or oscillatory solutions, having frequency and step length dependent parameters. As an example, we apply this analysis to a special class of numerical methods appeared in the literature, which are based on trigonometric polynomials.