Example 3.  Solve the I.V.P.   [Graphics:Images/RungeKuttaMod_gr_54.gif]  over  [Graphics:Images/RungeKuttaMod_gr_55.gif].  Use the Runge-Kutta method with  20  subintervals of  [0, 10]  to get a numerical approximation to the solution.  Plot the solution using the 21 points you just computed in the window {{0,10},{0,1}}.  Report the last point which is the numerical approximation to  (10, y(10)).
Solution 3.

[Graphics:../Images/RungeKuttaMod_gr_56.gif]

[Graphics:../Images/RungeKuttaMod_gr_57.gif]

[Graphics:../Images/RungeKuttaMod_gr_58.gif]

[Graphics:../Images/RungeKuttaMod_gr_59.gif]

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003