Explicit symplectic schemes to solve vortex systems (Q1309738)

A numerical scheme to solve an autonomous Hamiltonian system with the Hamiltonian \(H(p,q)\) is called symplectic if it preserves the symplectic structure, i.e. the mapping \((p(t),q(t))\to(p(t+\tau),q(t+\tau))\) is a canonical transformation for the time step \(\tau\). In this paper, based on a fourth-order Runge-Kutta scheme, the authors construct some explicit symplectic schemes for \(N\)-vortex plane flow systems with arbitrary \(N\). Selected numerical results illustrate the method in the case \(N=3\).