Some Fun With Julia Types: Symbolic Expressions in the ODE Solver
May 4 2017 in Differential Equations, Julia, Mathematics, Uncategorized | Tags: | Author: Christopher Rackauckas
In Julia, you can naturally write generic algorithms which work on any type which has specific “actions”. For example, an “AbstractArray” is a type which has a specific set of functions implemented. This means that in any generically-written algorithm that wants an array, you can give it an AbstractArray and it will “just work”. This kind of abstraction makes it easy to write a simple algorithm and then use that same exact code for other purposes. For example, distributed computing can be done by just passing in a DistributedArray, and the algorithm can be accomplished on the GPU by using a GPUArrays. Because Julia’s functions will auto-specialize on the types you give it, Julia automatically makes efficient versions specifically for the types you pass in which, at compile-time, strips away the costs of the abstraction.
This means … READ MORE
Building a Web App in Julia: DifferentialEquations.jl Online
January 17 2017 in Differential Equations, Julia, Mathematics | Tags: | Author: Christopher Rackauckas
Web apps are all the rage because of accessibility. However, there are usually problems with trying to modify some existing software to be a web app: specifically user interface and performance. In order for a web application to perform well, it must be able to have a clean user interface with a “smart” backend which can automatically accommodate to the user’s needs, but also give back a nice looking response in under a second. This has typically limited the types of applications which can become responsive web applications.
Scientific software is one domain where user interface has been obstructive at best, and always in need of better performance. However, the programming language Julia has allowed us to build both an easy to use and highly performant ecosystem of numerical differential equation solvers over the last 8 months. Thus we had … READ MORE
6 Months of DifferentialEquations.jl: Where We Are and Where We Are Going
December 15 2016 in Differential Equations, Julia, Mathematics, Programming, Stochastics, Uncategorized | Tags: DifferentialEquations.jl, julia | Author: Christopher Rackauckas
So around 6 months ago, DifferentialEquations.jl was first registered. It was at first made to be a library which can solve “some” types of differential equations, and that “some” didn’t even include ordinary differential equations. The focus was mostly fast algorithms for stochastic differential equations and partial differential equations.
Needless to say, Julia makes you too productive. Ambitions grew. By the first release announcement, much had already changed. Not only were there ordinary differential equation solvers, there were many. But the key difference was a change in focus. Instead of just looking to give a production-quality library of fast methods, a major goal of DifferentialEquations.jl became to unify the various existing packages of Julia to give one user-friendly interface.
Since that release announcement, we have made enormous progress. At this point, I believe we have both the most expansive and flexible … READ MORE
Introducing DifferentialEquations.jl
August 1 2016 in Differential Equations, FEM, Julia, Programming, Stochastics | Tags: DifferentialEquations.jl, julia | Author: Christopher Rackauckas
Edit: This post is very old. See this post for more up-to-date information.
Differential equations are ubiquitous throughout mathematics and the sciences. In fact, I myself have studied various forms of differential equations stemming from fields including biology, chemistry, economics, and climatology. What was interesting is that, although many different people are using differential equations for many different things, pretty much everyone wants the same thing: to quickly solve differential equations in their various forms, and make some pretty plots to describe what happened.
The goal of DifferentialEquations.jl is to do exactly that: to make it easy solve differential equations with the latest and greatest algorithms, and put out a pretty plot. The core idea behind DifferentialEquations.jl is that, while it is easy to describe a differential equation, they have such diverse behavior that experts have spent over a century compiling … READ MORE