Comparison among Correction Methods of Individual Kepler Energies in<i>n</i>-Body Simulations

Abstract

We develop a brand-new method of manifold correction that extends Nacozy's approach to correcting individual Kepler energies that vary with time in n-body problems of planetary dynamics. Besides discussing this method, we also closely study other existing manifold correction techniques, including the two scaling methods of Fukushima and Liu & Liao. We give a detailed discussion about them analytically and numerically. Our numerical experiments show that all three methods are effective and work almost equivalently in raising the precision of the numerical integration when the adopted basic integrators can give sufficient precision to chosen integrals or quasi-integrals. For simplicity of application, Liu & Liao's approach is worth recommending. However, this approach cannot improve the orbital eccentricity at all. Because of this, we prefer to use this brand-new extension, as well as the scaling method of Fukushima.