Gaussian quadrature rules and -stability of Galerkin schemes for ODE.
General linear methods: connection to one step methods and invariant curves.
Generalized interpolation and some applications in ordinary differential equations
Generalized periodic overimplicit multistep methods (GPOM methods)
The paper deals with some new methods for the numerical solution of initial value problems for ordinary differential equations. The main idea of these methods consists in the fact that in one step of the method a group of unknown values of the approximate solution is computed simultaneously. The class of methods under investigation is wide enough to contain almost all known classical methods. Sufficient conditions for convergence are found.
Generalized Runge-Kutta Methods of Order Four with Stepsize Control for Stiff Ordinary Differential Equations.
Geometric integrators for piecewise smooth Hamiltonian systems
In this paper, we consider C1,1 Hamiltonian systems. We prove the existence of a first derivative of the flow with respect to initial values and show that it satisfies the symplecticity condition almost everywhere in the phase-space. In a second step, we present a geometric integrator for such systems (called the SDH method) based on B-splines interpolation and a splitting method introduced by McLachlan and Quispel [Appl. Numer. Math. 45 (2003) 411–418], and we prove it is convergent, and that...
Global error control for the continuous Galerkin finite element method for ordinary differential equations
Global error estimation in the numerical solution of retarded differential equations by Euler's method
In this paper Zadunaisky's technique is used to estimate the global error propagated in the numerical solution of the system of retarded differential equations by Euler's method. Some numerical examples are given.