Parareal Algorithm Implementation and Simulation in Julia

We present a full implementation of the parareal algorithm—an integration technique to solve di erential equations in parallel— in the Julia programming language for a fully general, rst-order, initial-value problem. Our implementation accepts both coarse and ne 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.