Please wrire a program in Python! RK- Runge Kutta method and please PERFORM THE SYMPLECTIC METHOD AS WELL!

Use the RK as well as the symplectic method to calculate the trajectories of a particle of mass m=1 for the following double well potential, V(q)=0.15q4q2 Consider two cases: (a) (q0,p0)=(1,0) (b) (q0,p0)=(2.59,0) Use a stepsize of t=0.1s and calculate 1000 revolutions of the particle. Plot the first and the last revolution in phase space. Furthermore, calculate the revolution times, plot them and explain the behavior of your results. Remark: Since storing the momenta of each time step of a long-term trajectory requires a lot of memory, one would - in practice - perform the calculation of the revolution time during the ODE-solving (where in each step the momenta pn and pn+1 are compared). However, to keep the tasks of this assignment separated, we do that as a kind of a post-processing step here