Parareal Algorithm Implementation and Simulation in Julia

We present a full implementation of the parareal algorithm—an integration technique to solve differential equations in parallel—in the Julia programming language for a fully general, first-order, initial-value problem. We provide a brief overview of Julia—a concurrent programming language for scientific computing. Our implementation of the parareal algorithm accepts both coarse and fine integrators as functional arguments. We use Euler’s method and another Runge-Kutta integration technique as the integrators in our experiments. We also present a simulation of the algorithm for purposes of pedagogy and as a tool for investigating the performance of the algorithm.