Dedalus solves differential equations using spectral methods.
It's open-source, written in Python, and MPI-parallelized.
We develop and use Dedalus to study fluid dynamics, but it's designed to solve initial-value, boundary-value, and eigenvalue problems involving nearly arbitrary equations sets. You build a spectrally-representable domain, symbolically specify equations and boundary conditions, select a numerical solver, and go.
Flexibility
Dedalus implements a highly flexible spectral framework that can simulate many domains and custom equations.
Performance
Dedalus calls compiled libraries for performance-critical routines, and is MPI-parallelized.
Open Development
Dedalus is free and open-source software based on the scientific Python stack.