Adaptive Stepsize Control for Extrapolation Semi-Implicit Multistep ODE Solvers

Triangularly Implicit Iteration Methods for ODE-IVP Solvers

It often happens that iteration processes used for solving the implicit relations arising in ODE-IVP methods only start to converge rapidly after a certain number of iterations. Fast convergence right from the beginning is particularly important if we want to use so-called step-parallel iteration in which the iteration method is concurrently applied at a number of step points. In this paper, we...

Dynamical Systems and Adaptive Timestepping Ode Solvers

Initial value problems for ODEs are often solved numerically using adap-tive timestepping algorithms. We formulate a large class of such algorithms as discrete dynamical systems which are discontinuous and of higher dimension than the underlying ODE. By assuming suuciently strong nite-time convergence results on some neighbourhood of an attractor of the ODE we prove existence and upper semicont...

Experiments in stepsize control for Adams linear multistep methods

Implicit ODE solvers with good local error control for the transient analysis of Markov models

Obtaining the transient probability distribution vector of a continuous-time Markov chain (CTMC) using an implicit ordinary differential equation (ODE) solver tends to be advantageous in terms of run-time computational cost when the product of the maximum output rate of the CTMC and the largest time of interest is large. In this paper, we show that when applied to the transient analysis of CTMC...

Stepsize control for adaptive multiprecision path tracking

Numerical difficulties encountered when following paths using methods such as homotopy continuation may be overcome by combining adaptive stepsize and adaptive multiprecision. In the paper Adaptive multiprecision path tracking [1], precision and stepsize are adapted separately. This can lead to suboptimal performance and even failure in certain circumstances. This paper presents a strategy for ...