Example 2.  Solve  [Graphics:Images/RungeKuttaFehlbergMod_gr_44.gif]  with  [Graphics:Images/RungeKuttaFehlbergMod_gr_45.gif]  over  [Graphics:Images/RungeKuttaFehlbergMod_gr_46.gif].  Use Mathematica's NDSolve procedure.

Solution 2.

Compute Mathematica's solution using the built in procedure NDSolve.

[Graphics:../Images/RungeKuttaFehlbergMod_gr_47.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_48.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_49.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_50.gif]

Compare the solution using RKF45 with Mathematica's procedure NDSolve.
Look at the two solution curves.

[Graphics:../Images/RungeKuttaFehlbergMod_gr_51.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_52.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_53.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_54.gif]

[Graphics:../Images/RungeKuttaFehlbergMod_gr_55.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004