General linear methods for y′′ = f (y (t))

@article{DAmbrosio2012GeneralLM,
  title={General linear methods for y′′ = f (y (t))},
  author={Raffaele D'Ambrosio and Emanuele Giuseppe Esposito and Beatrice Paternoster},
  journal={Numerical Algorithms},
  year={2012},
  volume={61},
  pages={331-349}
}
In this paper we consider the family of General Linear Methods (GLMs) for the numerical solution of special second order Ordinary Differential Equations (ODEs) of the type y′′ = f(y(t)), with the aim to provide a unifying approach for the analysis of the properties of consistency, zero-stability and convergence. This class of methods properly includes all the classical methods already considered in the literature (e.g. linear multistep methods, Runge–Kutta–Nyström methods, two-step hybrid… CONTINUE READING
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