Direct event location techniques based on Adams multistep methods for discontinuous ODEs

Direct event location techniques based on Adams multistep methods for discontinuous ODEs

We investigate numerical techniques to locate the event points of the differential system x′ = f(x), characterized by a vector field f which is a discontinuous function along an event surface Σ = {x ∈ R| h(x) = 0} splitting the state space into two different regions R1 and R2, particularly f(x) = fi(x) when x ∈ Ri, for i = 1, 2 and f1(x) 6= f2(x) when x ∈ Σ. We propose event location techniques...

Exponential multistep methods of Adams-type

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. ...

Experiments in stepsize control for Adams linear multistep methods

Multistep Methods for Markovian Event Systems

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 integration of stiff systems of ODEs using multistep methods

The second order Ordinary Differential Equation (ODE) system obtained after semidiscretizing the wavetype Partial Differential Equation (PDE) with the Finite Element Method (FEM), shows strong numerical stiffness. Although it can be integrated using Matlab ode-solvers, the function ode15s offered by Matlab for solving stiff ODE systems does not result very efficient as its resolution requires t...