![[Graphics:Images/PainlevePropertyMod_gr_203.gif]](../Images/PainlevePropertyMod_gr_203.gif){kind=small}
with ![[Graphics:Images/PainlevePropertyMod_gr_204.gif]](../Images/PainlevePropertyMod_gr_204.gif){kind=small}
over
the interval ![[Graphics:Images/PainlevePropertyMod_gr_205.gif]](../Images/PainlevePropertyMod_gr_205.gif){kind=small}
. Example
7. Use the
extended Runge-Kutta method to compute a numerical approximation
for
with over
the interval .
Solution 7.
The companion
differential equation is ![[Graphics:../Images/PainlevePropertyMod_gr_206.gif]](../Images/PainlevePropertyMod_gr_206.gif){kind=small}
where ![[Graphics:../Images/PainlevePropertyMod_gr_207.gif]](../Images/PainlevePropertyMod_gr_207.gif){kind=small}
.
![[Graphics:../Images/PainlevePropertyMod_gr_208.gif]](../Images/PainlevePropertyMod_gr_208.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_209.gif]](../Images/PainlevePropertyMod_gr_209.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_210.gif]](../Images/PainlevePropertyMod_gr_210.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_211.gif]](../Images/PainlevePropertyMod_gr_211.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_212.gif]](../Images/PainlevePropertyMod_gr_212.gif){kind=small}
![[Graphics:../Images/PainlevePropertyMod_gr_213.gif]](../Images/PainlevePropertyMod_gr_213.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_214.gif]](../Images/PainlevePropertyMod_gr_214.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_215.gif]](../Images/PainlevePropertyMod_gr_215.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_216.gif]](../Images/PainlevePropertyMod_gr_216.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_217.gif]](../Images/PainlevePropertyMod_gr_217.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_218.gif]](../Images/PainlevePropertyMod_gr_218.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_219.gif]](../Images/PainlevePropertyMod_gr_219.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_220.gif]](../Images/PainlevePropertyMod_gr_220.gif)
(c) John H. Mathews 2005