Numerically integrate the Lane-Emden equation using the 4th order Runge-Kutta method.
To download the files, navigate to the directory where you want the folder in terminal, then type: git clone https://github.com/ellawang44/runge_kutta_lane_emden
To run the program, simply type python main.py in the terminal. This will run the numerical integration for n = 0.
There are optional arguments which will change the numerical integration being run and the outputs produced by the program.
To change the order of the Lane-Emden function being integrated, use the flag -n or --nthorder. e.g: '-n 1' will change the order to 1.
To change the time step per integration, use the flag -t or --tstep. e.g: -t 0.01 will change the time step to 0.01.
To plot the analytical solution for n=0 and n=1 on the same graph as the numerical solution, use the flag --check. Note that this is only valid for n=0 and n=1 as other values of n do not have an analytical solution.
To print the value of \xi and \frac{d \theta}{d \xi} at \xi = \xi_1 (i.e at \theta = 0), use the flag --eval.
This program was written in Python, and runs on both Python 2 and 3 producing identical results.
The required Python packages include: matplotlib.pyplot, numpy, and argparse