This release covers the completion of another successful summer. We have now completed a new round of tooling for solving large stiff and sparse differential equations. Most of this is covered in the exciting….

New Tutorial: Solving Stiff Equations for Advanced Users!

That is right, we now have a new tutorial added to the documentation on solving stiff differential equations. This tutorial goes into depth, showing how to use our recent developments to do things like automatically detect and optimize a solver with respect to sparsity pattern, or automatically symbolically calculate a Jacobian from a numerical code. This should serve...

Specifying parallel_type has been deprecated and a deprecation warning is thrown mentioning this. So don’t worry: your code will work but will give warnings as to what to change. Additionally, the DiffEqMonteCarlo.jl package is no longer necessary for any of this functionality.

Sparsity Performance: Jacobian coloring with numerical and forward differentiation

If you have a function f!(du,u) which has a Tridiagonal Jacobian, you could calculate that Jacobian by mixing perturbations. For example, instead of doing u .+ [epsilon,0,0,0,0,0,0,0,…], you’d do u .+ [epsilon,0,0,epsilon,0,0,…]. Because the epsilons will never overlap, you can then decode this “compressed” Jacobian into the sparse form. Do that 3 times and boom, full Jacobian in 4 calls to f! no matter the size of u! Without a color vector, this matrix would take 1+length(u) f! calls, so I’d say that’s a pretty good speedup.

Well, we zoomed towards this one. In this release we have a lot of very compelling
new features for performance in specific domains. Large ODEs, stiff SDEs, high
accuracy ODE solving, many callbacks, etc. are all specialized on and greatly
improved in this PR.

This is a huge release. We should take the time to thank every contributor to the JuliaDiffEq package ecosystem. A lot of this release focuses on performance features. The ability to use stiff ODE solvers on the GPU, with automated tooling for matrix-free Newton-Krylov, faster broadcast, better Jacobian re-use algorithms, memory use reduction, etc. All of these combined give some pretty massive performance boosts in the area of medium to large sized highly stiff ODE systems. In addition, numerous robustness fixes have enhanced the usability of these tools, along with a few new features like an implementation of extrapolation for...