Example 4.  Determine the error for the RKF45 solution that was found in Example 1.

Solution 4.

Get the abscissas and ordinates out of the data structure of the points in the RKF45 solution.  

[Graphics:../Images/RungeKuttaFehlbergMod_gr_70.gif]
[Graphics:../Images/RungeKuttaFehlbergMod_gr_71.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_72.gif]
[Graphics:../Images/RungeKuttaFehlbergMod_gr_73.gif]

Evaluate the "true solution" at the abscissas.  

[Graphics:../Images/RungeKuttaFehlbergMod_gr_74.gif]
[Graphics:../Images/RungeKuttaFehlbergMod_gr_75.gif]

Look at the [Graphics:../Images/RungeKuttaFehlbergMod_gr_76.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_77.gif]
[Graphics:../Images/RungeKuttaFehlbergMod_gr_78.gif]

Find the maximum error.

[Graphics:../Images/RungeKuttaFehlbergMod_gr_79.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_80.gif]



[Graphics:../Images/RungeKuttaFehlbergMod_gr_81.gif]


[Graphics:../Images/RungeKuttaFehlbergMod_gr_82.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_83.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_84.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004