Example 11.  Solve the I.V.P.  [Graphics:Images/RungeKuttaMod_gr_155.gif].    Compute the Runge-Kutta solution to the I.V.P.

Solution 11.

[Graphics:../Images/RungeKuttaMod_gr_156.gif]

[Graphics:../Images/RungeKuttaMod_gr_157.gif]

[Graphics:../Images/RungeKuttaMod_gr_158.gif]
[Graphics:../Images/RungeKuttaMod_gr_159.gif]
[Graphics:../Images/RungeKuttaMod_gr_160.gif]
[Graphics:../Images/RungeKuttaMod_gr_161.gif]
[Graphics:../Images/RungeKuttaMod_gr_162.gif]


[Graphics:../Images/RungeKuttaMod_gr_163.gif]

[Graphics:../Images/RungeKuttaMod_gr_164.gif]

[Graphics:../Images/RungeKuttaMod_gr_165.gif]
[Graphics:../Images/RungeKuttaMod_gr_166.gif]
[Graphics:../Images/RungeKuttaMod_gr_167.gif]
[Graphics:../Images/RungeKuttaMod_gr_168.gif]
[Graphics:../Images/RungeKuttaMod_gr_169.gif]


[Graphics:../Images/RungeKuttaMod_gr_170.gif]

[Graphics:../Images/RungeKuttaMod_gr_171.gif]

[Graphics:../Images/RungeKuttaMod_gr_172.gif]
[Graphics:../Images/RungeKuttaMod_gr_173.gif]
[Graphics:../Images/RungeKuttaMod_gr_174.gif]
[Graphics:../Images/RungeKuttaMod_gr_175.gif]
[Graphics:../Images/RungeKuttaMod_gr_176.gif]

Animation 1.  ( Runge-Kutta Method of Order 4  Runge-Kutta Method of Order 4 ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004