Author Archives: JuliaDiffEq

Stiff SDE and DDE Solvers

By: JuliaDiffEq

Re-posted from: http://juliadiffeq.org/2017/09/09/StiffDDESDE.html

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

By: JuliaDiffEq

Re-posted from: http://juliadiffeq.org/2017/08/13/SDIRK.html

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

By: JuliaDiffEq

Re-posted from: http://juliadiffeq.org/2017/07/07/SymplecticRosenbrock.html

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.