High-order predictor–corrector of exponential fitting for the N-body problems

We develop the seventh-step predictor–corrector of exponential fitting method for the N-body problems. We apply our proposed scheme to Kepler problem, the interaction of seven argon atoms in a plane and three particles bound together by two springs of different stiffnesses. The three problems have various potential functions. We demonstrate the accuracy and efficiency of our proposed scheme via comparison with other analytical and numerical results. The numerical results show that the schemes are highly accurate and computationally efficient.