The study of the sensitivity of the solution of a system of differential equations with respect to
changes in the initial conditions leads to the introduction of an adjoint system, whose …

We consider methods that integrate systems of differential equations dy/dt=f(y) by taking
advantage of a decomposition of the right-hand side f=∑f^ν. We derive a general necessary …

Multi-derivative one-step methods based upon Euler–Maclaurin integration formulae are
considered for the solution of canonical Hamiltonian dynamical systems. Despite the …

The study of the order conditions of numerical integrators for systems of differential
equations and differential-algebraic equations often leads to different kinds of series …

In the past few years there has been a substantial amount of research on symplectic
integration. The subject is only part of a program concerned with numerically preserving a …

A class of higher order methods is investigated which can be viewed as implicit Taylor series
methods based on Hermite quadratures. Improved automatic differentiation techniques for …

We consider the classical Taylor series approximation to the solution of initial value
problems in ordinary di erential equations and examine implicit variants for the numerical …

The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by
F. Loscalzo in 1968 for dealing with initial value problems is analyzed. Such schemes have …

This paper provides a brief history of B-series and the associated Butcher group and
presents the new theory of word series and extended word series. B-series (Hairer and …

We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK)
methods applied to systems of Hamiltonian ordinary differential equations by means of …