A class of explicit symmetric multistep methods is proposed for integrating the equations of motion of charged particles in an electro-magnetic field. The magnetic forces are built into these methods in a special way that respects the Lagrangian structure of the problem. It is shown that such methods approximately preserve energy and momentum over very long times, proportional to a high power o...

Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l]. Wallace and Gupta [13] have suggested a polynomial formulation of the usual first-derivative multistep methods. Recently ...

Multistep methods for firstand second-order ordinary differential equations are used for the full discretizations of standard Galerkin approximations to the initial-periodic boundary value problem for first-order linear hyperbolic equations in one space dimension and to the initial-boundary value problem for second-order lin2 ear selfadjoint hyperbolic equations in many space dimensions. L -err...

We consider multistep methods for accelerated trajectory generation in the simulation of Markovian event systems, which is particularly useful in cases where the length of trajectories is large, e.g. when regenerative cycles tend to be long, when we are interested in transient measures over a finite but large time horizon, or when multiple time scales render the system stiff. 1. Markovian Event...

The paper is concerned with the construction, implementation and numerical analysis of exponential multistep methods. These methods are related to explicit Adams methods but, in contrast to the latter, make direct use of the exponential and related matrix functions of a (possibly rough) linearization of the vector field. This feature enables them to integrate stiff problems explicitly in time. ...