An optimized Forest–Ruth-like algorithm in extended phase space

Abstract

An optimized fourth-order Forest–Ruth-like symplectic algorithm, which is based on a minimum of the norm of fifth-order truncation terms, was originally designed for separable Hamiltonian problems. With the aid of extended phase space methods, this algorithm is further reformulated to explicitly solve inseparable Hamiltonian systems. Although an extra permutation substep is included and destroys symplecticity in general, the method is symmetric and therefore resembles a symplectic integrator in conservation of the original Hamiltonian. In fact, our numerical tests show that the optimized algorithm combined with the midpoint permutations always enhances the quality of numerical integrations in comparison with the corresponding nonoptimized counterpart for inseparable Hamiltonian problems. As a result, the optimized algorithm is worth recommending in application.