Symplectic Integrators: Preserving Order in Dynamic Systems, from Black Holes to Ice Fishing
Symplectic integrators are specialized numerical methods designed to preserve the geometric structure inherent in Hamiltonian systems—systems governed by energy-conserving dynamics. Unlike generic solvers, they uphold the symplectic 2-form, a cornerstone of phase space geometry, ensuring long-term stability and accuracy in complex simulations. This preservation is crucial because even small numerical errors can amplify over time,…
