An n-body problem solver with Runge-Kutta-Fehlberg method (RKF45).
Assume there are
By Newton's laws, we have
Discretize the differential equations
Let
It is similar to RK4 method, but with adaptive step length adjustment.
OJ problem and solution motivation: 洛谷 P3945 三体问题
ODE numerical solution methods: Runge-Kutta Methods, Runge–Kutta–Fehlberg method