Example 1.  Solve the van der Pol equation with  [Graphics:Images/VanDerPolMod_gr_19.gif].  
    [Graphics:Images/VanDerPolMod_gr_20.gif].  

Solution 1.

Enter the functions  [Graphics:../Images/VanDerPolMod_gr_21.gif]  and  [Graphics:../Images/VanDerPolMod_gr_22.gif]  and form the vector function  [Graphics:../Images/VanDerPolMod_gr_23.gif].  

[Graphics:../Images/VanDerPolMod_gr_24.gif]


[Graphics:../Images/VanDerPolMod_gr_25.gif]

 

 

Compute the Runge-Kutta solution.

[Graphics:../Images/VanDerPolMod_gr_26.gif]


[Graphics:../Images/VanDerPolMod_gr_27.gif]

[Graphics:../Images/VanDerPolMod_gr_28.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004