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An accurate and efficient method dealing with the few-body dynamics isimportant for simulating collisional N-body systems like star clusters and tofollow the formation and evolution of compact binaries. We describe such amethod which combines the time-transformed explicit symplectic integrator(Preto & Tremaine 1999; Mikkola & Tanikawa 1999) and the slow-down method(Mikkola & Aarseth 1996). The former conserves the Hamiltonian and the angularmomentum for a long-term evolution, while the latter significantly reduces thecomputational cost for a weakly perturbed binary. In this work, the Hamiltonequations of this algorithm are analyzed in detail. We mathematically andnumerically show that it can correctly reproduce the secular evolution like theorbit averaged method and also well conserve the angular momentum. For a weaklyperturbed binary, the method is possible to provide a few order of magnitudefaster performance than the classical algorithm. A publicly available codewritten in the c++ language, SDAR, is available on GitHub(https://github.com/lwang-astro/SDAR). It can be used either as a stand alonetool or a library to be plugged in other $N$-body codes. The high precision ofthe floating point to 62 digits is also supported.

A slow-down time-transformed symplectic integrator for solving the few-body problem