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
An efficient numerical method for highly oscillatory ordinary differential equations.
An efficient numerical method for highly oscillatory ordinary differential equations.
Stability regions of one step mixed collocation methods for y" = f (x, y)
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
Stability regions of one step mixed collocation methods for y″=f(x,y)
Applied Numerical Mathematics
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We present a symbolic-numerical package to analyze the linear stability properties of Runge-Kutta-Nyström 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.