Consider the following Van der Pol equation

y" - μ(y² - 1)y' + y = 0,     μ > 0;     y(0) = 0,    y(2) = 1,        (1)

which governs the flow of current in a vacuum tube with three internal elements. Let h = 0.1 and μ = 0.1, 1, 2, respectively.

(a) Use the Shooting method with Newton's method and TOL = 10^-4 to derive a IVP system solved by RK4, and find approximated solutions to (1).

(b) Use Finite-Difference method to derive a nonlinear system, which is solved by Newton's method discussed in class, and then find approximated solutions to (1).

By plotting the graphs for (x, y(x)) in Part (a) and (b), what have you discovered about the solution with respect to μ?

Requirements: Submit to CCLE a file lastaame_firstname_hw6.zip containing the following files:

• A MATLAB function shoot.m that implements the Nonlinear Shooting method, a MATLAB function fd.m that implements the Nonlinear Finite-Difference method, and a MATLAB script main.m that solves the given BVP and plots the approximated solutions.
• A PDF report that shows the plots and answers the above questions.