The continuous approximations play a vital role in N-body simulations. We constructed three different types, namely, one-step (cubic and quintic Hermite), two-step, and three-step Hermite interpolation schemes. The continuous approximations obtained by Hermite interpolation schemes and interpolants for ODEX2 and ERKN integrators are discussed in this paper. The primary focus of this paper is to measure the accuracy and computational cost of different types of interpolation schemes for a variety of gravitational problems. The gravitational problems consist of Kepler’s two-body problem and the more realistic problem involving the Sun and four gas-giants—Jupiter, Saturn, Uranus, and Neptune. The numerical experiments are performed for the different integrators together with one-step, two-step, and three-step Hermite interpolation schemes, as well as the interpolants.
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