Example 4.  For the  I.V.P.  
    [Graphics:Images/Lotka-VolterraMod_gr_227.gif]   with   [Graphics:Images/Lotka-VolterraMod_gr_228.gif],  
and
    [Graphics:Images/Lotka-VolterraMod_gr_229.gif]   with   [Graphics:Images/Lotka-VolterraMod_gr_230.gif].    
Show that the numerical solution in Example 3 and the analytic solution in Example 4 are in agreement.

Solution 4.

[Graphics:../Images/Lotka-VolterraMod_gr_231.gif]


[Graphics:../Images/Lotka-VolterraMod_gr_232.gif]

[Graphics:../Images/Lotka-VolterraMod_gr_233.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_234.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_235.gif]



[Graphics:../Images/Lotka-VolterraMod_gr_236.gif]


[Graphics:../Images/Lotka-VolterraMod_gr_237.gif]

[Graphics:../Images/Lotka-VolterraMod_gr_238.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_239.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_240.gif]


Or we could plot several curves for the implicit solution  [Graphics:../Images/Lotka-VolterraMod_gr_241.gif].  

[Graphics:../Images/Lotka-VolterraMod_gr_242.gif]


[Graphics:../Images/Lotka-VolterraMod_gr_243.gif]

[Graphics:../Images/Lotka-VolterraMod_gr_244.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_245.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_246.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_247.gif]
[Graphics:../Images/Lotka-VolterraMod_gr_248.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004