A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

Abstract

This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q″(t)+Mq(t)=f(q(t)) with a symmetric and positive semi-definite matrix M and f(q)=−∇U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p,q)=12pTp+12qTMq+U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi–Pasta–Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method.