JAM: The Jacobian Analytical Method
JAM is a powerful numerical method for solving complex non-linear problems, particularly in fluid dynamics with free interfaces. It leverages analytical Jacobians to achieve high efficiency and accuracy across implementations in Python, Matlab, and Julia.
Reference
Herrada, M.A., Montanero, J.M., 2016. A numerical method to study the dynamics of capillary fluid systems. Journal of Computational Physics, 306, pp.137-147.