A fourth-order energy-preserving and symmetric average vector field integrator with low regularity assumption

Abstract

It is known that the average vector field (AVF) integrator is energy-preserving but only with second-order accuracy. Motivated by the construction of the classical AVF integrator, we devoted to constructing and analysing of high-order energy-preserving integrators for the second-order Hamiltonian systems in this work. Firstly, a novel improved average vector field (IAVF) integrator is derived by modifying the average vector field of the AVF integrator. Then the energy preservation and symmetry of the derived IAVF integrator are rigorously studied. Another significant investigation of the paper is that the IAVF integrator is shown to converge with order four under low regularity assumption q(t)∈C3([t0,T]). Numerical experiments are conducted to demonstrate the remarkable superiority in accuracy and efficiency over the traditional AVF integrator. Numerical results confirm the conclusions of our theoretical analysis.