Collocation for finding periodic orbits of ODEs

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....

2020-05-01

Working with broadcasting in Julia

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....

2019-01-16

BarycentricInterpolation.jl

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!...

2018-12-04