Julia

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. If you want to know more about these types of spectral methods, take a look at the excellent (and short!) introduction by Trefethen in “Spectral Methods in MATLAB”, SIAM 2000. If you want more detail then the magnum opus by Boyd “Chebyshev and Fourier Spectral Methods”, Dover 2001 (freely available on his personal website) is also very good. ...

Broadcasting in Julia is a way of writing vectorised code (think Matlab) that is performant and explicit. The benefits of performant code are obvious (faster!) but explicit vectorisation is also a significant benefit. When I first saw Matlab and how you could call the sin with a vector input, I was (slightly) blown away by the usefulness of this. It didn’t take too long for me to realise the limitations though; vectorising a complicated function can require quite a bit of code gymnastics, which doesn’t usually help the readability, particularly for those students who are relatively new to programming. ...

Over the past couple of years or so I’ve been getting into the Julia programming language; it’s been great to watch the language mature over time. Many people proclaim the virtues of its speed (it’s very fast for a dynamic language) but really I like its elegance - it’s a very well designed language that makes full use of multiple dispatch. (Multiple dispatch is something that I doubt most coders know much about but once you are used to it, it’s indispensable!) ...