![[Graphics:Images/PainlevePropertyMod_gr_239.gif]](../Images/PainlevePropertyMod_gr_239.gif){kind=small}
with ![[Graphics:Images/PainlevePropertyMod_gr_240.gif]](../Images/PainlevePropertyMod_gr_240.gif){kind=small}
over
the interval ![[Graphics:Images/PainlevePropertyMod_gr_241.gif]](../Images/PainlevePropertyMod_gr_241.gif){kind=small}
. Example
9. Use the
extended Runge-Kutta method to compute a numerical approximation
for
with over
the interval .
Solution 9.
![[Graphics:../Images/PainlevePropertyMod_gr_242.gif]](../Images/PainlevePropertyMod_gr_242.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_243.gif]](../Images/PainlevePropertyMod_gr_243.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_244.gif]](../Images/PainlevePropertyMod_gr_244.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_245.gif]](../Images/PainlevePropertyMod_gr_245.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_246.gif]](../Images/PainlevePropertyMod_gr_246.gif){kind=small}
![[Graphics:../Images/PainlevePropertyMod_gr_247.gif]](../Images/PainlevePropertyMod_gr_247.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_248.gif]](../Images/PainlevePropertyMod_gr_248.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_249.gif]](../Images/PainlevePropertyMod_gr_249.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_250.gif]](../Images/PainlevePropertyMod_gr_250.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_251.gif]](../Images/PainlevePropertyMod_gr_251.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_252.gif]](../Images/PainlevePropertyMod_gr_252.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_253.gif]](../Images/PainlevePropertyMod_gr_253.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_254.gif]](../Images/PainlevePropertyMod_gr_254.gif)
(c) John H. Mathews 2005