Example 3.  Plot the error for Milne-Simpson's method.

Solution 3.

[Graphics:../Images/MilneSimpsonMod_gr_67.gif]

[Graphics:../Images/MilneSimpsonMod_gr_68.gif]

[Graphics:../Images/MilneSimpsonMod_gr_69.gif]
and the step size h = 0.2


Since we have the analytic or "true solution" at hand, we can run experiments to verify that Milne-Simpson's method has order  [Graphics:../Images/MilneSimpsonMod_gr_71.gif].   Reduce the step size by  [Graphics:../Images/MilneSimpsonMod_gr_72.gif] and see what happens to the error.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004