Mathematics

My PhD was on the topic of delay differential equations (DDEs) and, at the time, I wrote lots of utilities to do things like calculate the stability of linearised equations. All that code has been lost to the mists of time but I still have call for it every now and again (e.g., for real-time dynamic substructuring where I need to model the delays in the control loop). Here is some code in Julia that calculates the stability of a DDE in the form...

Every now and again I’m asked how to compute the periodic orbits of ODEs using a boundary value solver. Each time, I go looking for old code that does this and, each time, I can’t find it and end up rewriting the collocation code from scratch. This time I thought I’d put my code here so that I have a better chance of finding it again in the future! The basic idea is to use a Fourier differentiation matrix to approximate the derivatives along the orbit and use a nonlinear solver to ensure that those derivatives match the vector field....