Adjustment of Force–Gradient Operator in Symplectic Methods

Many force–gradient explicit symplectic integration algorithms have been designed for the Hamiltonian H=T(p)+V(q) with kinetic energy T(p)=p2/2 in existing references. When a operator is appropriately adjusted as new operator, it still suitable class of problems H=K(p,q)+V(q) integrable part K(p,q)=?i=1n?j=1naijpipj+?i=1nbipi, where aij=aij(q) and bi=bi(q) are functions coordinates q. The newly not but similar to momentum-version associated potential V. extended (or adjusted) no longer solvers original Hamiltonian, slightly modified Hamiltonians. They integrators symmetry or time reversibility. Numerical tests show that standard without generally poorer than corresponding methods computational accuracies efficiencies. optimized better non-optimized counterparts. Among tested methods, two seven-stage fourth-order Omelyan, Mryglod Folk exhibit best numerical performance. As result, one used study orbital dynamical features Hénon–Heiles system spring pendulum. These allow integrations problems, such spiral structure self-consistent models rotating galaxies arms galaxies.