![[Graphics:Images/PainlevePropertyMod_gr_287.gif]](../Images/PainlevePropertyMod_gr_287.gif){kind=small}
with ![[Graphics:Images/PainlevePropertyMod_gr_288.gif]](../Images/PainlevePropertyMod_gr_288.gif){kind=small}
over the
interval ![[Graphics:Images/PainlevePropertyMod_gr_289.gif]](../Images/PainlevePropertyMod_gr_289.gif){kind=small}
. Example
12. Use the
extended Runge-Kutta method to compute a numerical approximation
for
with
over the
interval .
Solution 12.
![[Graphics:../Images/PainlevePropertyMod_gr_290.gif]](../Images/PainlevePropertyMod_gr_290.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_291.gif]](../Images/PainlevePropertyMod_gr_291.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_292.gif]](../Images/PainlevePropertyMod_gr_292.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_293.gif]](../Images/PainlevePropertyMod_gr_293.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_294.gif]](../Images/PainlevePropertyMod_gr_294.gif){kind=small}
![[Graphics:../Images/PainlevePropertyMod_gr_295.gif]](../Images/PainlevePropertyMod_gr_295.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_296.gif]](../Images/PainlevePropertyMod_gr_296.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_297.gif]](../Images/PainlevePropertyMod_gr_297.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_298.gif]](../Images/PainlevePropertyMod_gr_298.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_299.gif]](../Images/PainlevePropertyMod_gr_299.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_300.gif]](../Images/PainlevePropertyMod_gr_300.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_301.gif]](../Images/PainlevePropertyMod_gr_301.gif)
![[Graphics:../Images/PainlevePropertyMod_gr_302.gif]](../Images/PainlevePropertyMod_gr_302.gif)
(c) John H. Mathews 2005