Example 11.  Use the extended Runge-Kutta method to compute a numerical approximation for  

            [Graphics:Images/PainlevePropertyMod_gr_271.gif]   with  [Graphics:Images/PainlevePropertyMod_gr_272.gif]   over the interval  [Graphics:Images/PainlevePropertyMod_gr_273.gif].  

Solution 11.

[Graphics:../Images/PainlevePropertyMod_gr_274.gif]

[Graphics:../Images/PainlevePropertyMod_gr_275.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_276.gif]

[Graphics:../Images/PainlevePropertyMod_gr_277.gif]

[Graphics:../Images/PainlevePropertyMod_gr_278.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_279.gif]

[Graphics:../Images/PainlevePropertyMod_gr_280.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_281.gif]

[Graphics:../Images/PainlevePropertyMod_gr_282.gif]

[Graphics:../Images/PainlevePropertyMod_gr_283.gif]

 

 

[Graphics:../Images/PainlevePropertyMod_gr_284.gif]

[Graphics:../Images/PainlevePropertyMod_gr_285.gif]

[Graphics:../Images/PainlevePropertyMod_gr_286.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005