Example 10.   Use the extended Runge-Kutta method to compute a numerical approximation for  

            [Graphics:Images/PainlevePropertyMod_gr_255.gif]   with   [Graphics:Images/PainlevePropertyMod_gr_256.gif]   over the interval  [Graphics:Images/PainlevePropertyMod_gr_257.gif].  

Solution 10.

[Graphics:../Images/PainlevePropertyMod_gr_258.gif]

[Graphics:../Images/PainlevePropertyMod_gr_259.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_260.gif]

[Graphics:../Images/PainlevePropertyMod_gr_261.gif]

[Graphics:../Images/PainlevePropertyMod_gr_262.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_263.gif]

[Graphics:../Images/PainlevePropertyMod_gr_264.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_265.gif]

[Graphics:../Images/PainlevePropertyMod_gr_266.gif]

[Graphics:../Images/PainlevePropertyMod_gr_267.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_268.gif]

[Graphics:../Images/PainlevePropertyMod_gr_269.gif]

[Graphics:../Images/PainlevePropertyMod_gr_270.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005