A New Third-Order Explicit Symplectic Scheme For Hamiltonian Systems

Symplectic geometric algorithms are superior to other standard methods in preserving structures and long-time tracking ability when solving Hamiltonian systems, but the phase errors do accumulate. A fractional-step symmetric symplectic method (FSJS), composing low order schemes, is presented for separable Hamiltonian systems. A new third-order scheme derived from FSJS, is appropriate for engineering application, and its phase error is smaller than the well-known third-order symplectic Runge-Kutta (SRK3) scheme. Some numerical examples are given to show the efficiency of our scheme.