ABSTRACT
We are constructing a one-stage multistep-method for the numerical integration of the N-Body problem. The method has two desirable properties: trigonometrical-fitting and P-stability, which are crucial for long-term integration of systems of periodic IVPs. A reference solution has been generated for a long-time interval and the new method is being compared with recently constructed multistep methods. The results after integrating the five-outer planets problem shows the high efficiency of the new method.
