WIAS-PDELib/VoronoiFVM.jl

Grid-based approximation of partial differential equations in Julia

Automatic Finite Difference PDE solving with Julia SciML

Physics-Informed Neural Networks (PINN) Solvers of (Partial) Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

Firedrake is an automated system for the portable solution of partial differential equations using the finite element method (FEM)

FreeFEM source code

FiPy is a Finite Volume PDE solver written in Python

Tools for building fast, hackable, pseudospectral partial differential equation solvers on periodic domains

PyClaw is a Python-based interface to the algorithms of Clawpack and SharpClaw. It also contains the PetClaw package, which adds parallelism through PETSc.

Julia interface to Sundials, including a nonlinear solver (KINSOL), ODEs (CVODE and ARKODE), and DAEs (IDA)