JuliaCon 2017

DifferentialEquations.jl is a highly extendable high-performance library for solving a vast array of differential equations in Julia. The purpose of this workshop is to introduce the participants to DifferentialEquations.jl, focusing on the new types of problems that are able to be explored through this software and how Julia has made this possible. We will start with a tutorial of the ordinary differential equation solvers. Users will be shown how to use the common solver interface to solve and analyze equations using the solvers from OrdinaryDiffEq.jl, Sundials.jl, ODE.jl, LSODA.jl, and ODEInterface.jl. Next, the capabilities will be explored in further depth, and users will walk through solving hybrid differential equations continuous + discrete components), using arbitrary precision and unitful arithmetic, and solving equations with discontinuous events. After that, the tutorial will show users how to branch out to other forms of differential equations, showing how the same interface allows them to use the unique high-order adaptive Runge-Kutta methods for stochastic differential equations and the fast high-order methods for delay differential equations. Lastly, participants will be walked through the analysis add-on tools, using Optim.jl to perform parameter estimation of ordinary differential equation models, identify sensitive parameters, and quantify numerical uncertainties of solutions. Users will leave the workshop with an expanded view of what kinds of problems can be solved with DifferentialEquations.jl and with the knowledge of how to solve them.