I have to code the Runge-Kutta Method to solve a Bessel Function of the first kind. Here are some excerpts from the instructions of my assignment:
For the initial conditions go to WolframAlpha and,
- To eliminate the constant $c_2$ from equation
$$ y(x) = c_1 J_\alpha (x) + c_2 Y_\alpha (x) $$
(General solution to the Bessel equation)
And choose one of the zeros of the Bessel function using the function
BesselJZero[n, k]
, where $n$ is the desired value (I'm given n = 3.2), and $k$ is the $k$th zero of the Bessel function.
- To choose $c_1 = 1$, use the function
BesselJ[n,x]
to select the value of the function at some desired $x$-value.
This procedure will leave the $J_a(x)$ desired function. Don't forget to report the values used.
Questions:
I don’t understand how this procedure provides me with the initial values (i.e., the value of the function at a starting point and the value of its first derivative). Should I separate the second-order equation into a system of first-order equations?
Should I also use DSolve
from WolframAlpha?
Thank you so much in advance!