The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Two Step Runge-Kutta-Nyström Methods for y'' = f(x, y) and P-Stability
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Original article: Rosenbrock-type methods applied to discontinuous differential systems
Mathematics and Computers in Simulation
Exponentially fitted singly diagonally implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
P-stable general Nyström methods for y˝=f(y(t))
Journal of Computational and Applied Mathematics
Order conditions for General Linear Nyström methods
Numerical Algorithms
| Hi-index | 0.00 |
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驴驴驴=驴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 methods and two-step Runge---Kutta---Nyström methods) as special cases. We deal with formulation of GLMs and present some general results regarding consistency, zero-stability and convergence. The approach we use is the natural extension of the GLMs theory developed for first order ODEs.