Reduction of round-off errors in numerical integration of equation of motion using pair-precision technique

Calculation of numerical integration is realized with thousands of floating-point numbers and round-off errors accumulate as the number of steps increases in the integration. The aim of this study is to reduce the round-off errors accumulated in the numerical integration of Newtonian equation of motion using pair-precision technique. Pair-precision technique is frequently used in studies of the stability of the Solar System for the purpose to investigate dynamical processes with more precise results (Quinn and Tremaine 1989; Quinlan 1994; Rein and Spiegel 2015). Through this technique, a 105-bit precision integration was performed using 53-bit double-precision variables. The obtained results were compared with the results of double-precision test integration using two-body orbital constants and a gain of 8 digits has been achieved. Consequently, local integration errors were reduced 10^8 times despite by a factor of 3.01 CPU time cost of the technique.