New Directions in Numerical Computation

Exact Numerical Computation via Symbolic Computation

Precise numerical computation

Arithmetic systems such as those based on IEEE standards currently make no attempt to track the propagation of errors. However a formal error analysis can be complicated and is often confined to the realm of experts in numerical analysis. In recent years there has been a resurgence in interest in automated methods for accurately tracking the propagation of errors. In this article we will descri...

Numerical Computation of Rectangular

Numerical Computation of Canards

Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuat...

Numerical Computation of Normal

In this paper we introduce a general methodology for computing (numerically) the normal form around a periodic orbit of an autonomous analytic Hamiltonian system. The process follows two steps. First, we expand the Hamiltonian in suitable coordinates around the orbit and second, we perform a standard normal form scheme, based on the Lie series method. This scheme is carried out up to some nite ...