Stiff SDE and DDE Solvers

The end of the summer cycle means that many things, including Google Summer of Code projects, are being released. A large part of the current focus has been to develop tools to make solving PDEs easier, and also creating efficient tools for generalized stiff differential equations. I think we can claim to be one of the first libraries to include methods for stiff SDEs, one of the first for stiff DDEs, and one of the first to include higher order adaptive Runge-Kutta Nystrom schemes. And that’s not even looking at a lot of the more unique stuff in this release. Take a look.

SDIRK Methods

This has been a very productive summer! Let me start by saying that a relative newcomer to the JuliaDiffEq team, David Widmann, has been doing some impressive work that has really expanded the internal capabilities of the ordinary and delay differential equation solvers. Much of the code has been streamlined due to his efforts which has helped increase our productivity, along with helping us identify and solve potential areas of floating point inaccuracies. In addition, in this release we are starting to roll out some of the results of the Google Summer of Code projects. Together, there’s some really exciting stuff!

High Order Rosenbrock and Symplectic Methods

For awhile I have been saying that JuliaDiffEq really needs some fast high accuracy stiff solvers and symplectic methods to take it to the next level. I am happy to report that these features have arived, along with some other exciting updates. And yes, they benchmark really well. With new Rosenbrock methods specifically designed for stiff nonlinear parabolic PDE discretizations, SSPRK enhancements specifically for hyperbolic PDEs, and symplectic methods for Hamiltonian systems, physics can look at these release notes with glee. Here’s the full ecosystem release notes.

Filling In The Interop Packages and Rosenbrock

In the 2.0 state of the ecosystem post it was noted that, now that we have a clearly laid out and expansive common API, the next goal is to fill it in. This set of releases tackles the lowest hanging fruits in that battle. Specifically, the interop packages were setup to be as complete in their interfaces as possible, and the existing methods which could expand were expanded. Time for specifics.

DifferentialEquations.jl 2.0

This marks the release of ecosystem version 2.0. All of the issues got looked over. All (yes all!) of the API suggestions that were recorded in issues in JuliaDiffEq packages have been addressed! Below are the API changes that have occurred. This marks a really good moment for the JuliaDiffEq ecosystem because it means all of the long-standing planned API changes are complete. Of course new things may come up, but there are no more planned changes to core functionality. This means that we can simply work on new features in the future (and of course field bug reports as they come). A blog post detailing our full 2.0 achievements plus our 3.0 goals will come out at our one year anniversary. But for now I want to address what the API changes are, and the new features of this latest update.

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