Chris is an encyclopedia on ODEs. Take a look at this. No other system has this thorough a study of so many methods in one place.<p><a href="https://github.com/JuliaDiffEq/DiffEqDevTools.jl/blob/master/src/ode_tableaus.jl" rel="nofollow">https://github.com/JuliaDiffEq/DiffEqDevTools.jl/blob/master...</a><p>This is the kind of thing we imagined experts being able to do when we designed Julia. Having implemented some such solvers in the past, I can safely say this stuff is easily the best out there.
Chris — the author of this blog post and lead developer of the DifferentialEquations.jl ecosystem — had a really nice workshop at this year's JuliaCon. You can watch it online here: <a href="https://www.youtube.com/watch?v=75SCMIRlNXM" rel="nofollow">https://www.youtube.com/watch?v=75SCMIRlNXM</a>. His intro there is really approachable and even if you just watch the first 10 minutes you can come away with something tangible.
I see those Bombay Sapphires have been working towards a good cause!<p>But in all seriousness, the comparison was far more thorough than I expected going in. I learned quite a bit, and it's making me consider giving Julia another shot. I've been tinkering with mostly Rust lately, very happily, but this post makes me miss something with the strong scientific bend of Julia. So job well done and thanks for taking the time to write this.
Intel has an ODE solver [1] that seems <i>unbelievably</i> good at solving certain kinds of differential equations. I'm surprised/disappointed it wasn't even mentioned. I would've loved to see an evaluation of it against MATLAB (or other solvers) more than any other pair in the list.<p>[1] <a href="https://software.intel.com/en-us/articles/intel-ordinary-differential-equations-solver-library" rel="nofollow">https://software.intel.com/en-us/articles/intel-ordinary-dif...</a>
For a more "systems" approach for ODEs, you should look at Modelica: <a href="https://en.wikipedia.org/wiki/Modelica" rel="nofollow">https://en.wikipedia.org/wiki/Modelica</a> It's very powerful stuff.
Can anyone recommend any introductory material on real-world examples of differential equations? I don't mean the first-year undergrad textbook stuff with differential equations for population growth and chemical reactions and mechanics that can be solved via separation of variables etc. I mean descriptions of models used in science and engineering that result in needing to use the fancy solvers that this thread is discussing.
This seems to be all about ODEs. Has anyone got any recommendation for a good PDE solver? One that might run a problem having more than three spatial dimensions? (and ideally callable from Python)