Example

Use rk4plot to graphically investigate numerical solutions to the ODE $x'= 2tx$. Use the four step sizes $h = 0.5,\; 0.25,\; 0.1,\;, 0.01$. This M-file uses a 4th order Runge-Kutta scheme. Identify each plot with its respective step size.

1. Change only the following in initn.m

    
   ftx='2*t*x'; 
   hvec=[.5,.25,.1,.01]; 
   t0=-2; tf=2; x0=1;
   

   Save, then type initn to initialize the variables (or copy-and-paste at the Emporium).
2. Type rk4plot
   
   
   
   
   (How does the plot for eulplot compare with that for rk4plot when $h = 0.1$? Which is more accurate for the same step size?)