Example 9.  Solve the I.V.P.  [Graphics:Images/MilneSimpsonMod_gr_123.gif].  

Solution 9.

Compute the Milne-Simpson solution based on 50 subintervals and plot the results.

[Graphics:../Images/MilneSimpsonMod_gr_124.gif]


[Graphics:../Images/MilneSimpsonMod_gr_125.gif]
[Graphics:../Images/MilneSimpsonMod_gr_126.gif]


[Graphics:../Images/MilneSimpsonMod_gr_127.gif]

[Graphics:../Images/MilneSimpsonMod_gr_128.gif]

[Graphics:../Images/MilneSimpsonMod_gr_129.gif]
[Graphics:../Images/MilneSimpsonMod_gr_130.gif]
[Graphics:../Images/MilneSimpsonMod_gr_131.gif]
[Graphics:../Images/MilneSimpsonMod_gr_132.gif]
[Graphics:../Images/MilneSimpsonMod_gr_133.gif]

Compute the Milne-Simpson solution based on 100 subintervals and plot the results.
Observe that one fewer subinterval is computed for this case.

[Graphics:../Images/MilneSimpsonMod_gr_134.gif]

[Graphics:../Images/MilneSimpsonMod_gr_135.gif]

[Graphics:../Images/MilneSimpsonMod_gr_136.gif]
[Graphics:../Images/MilneSimpsonMod_gr_137.gif]
[Graphics:../Images/MilneSimpsonMod_gr_138.gif]
[Graphics:../Images/MilneSimpsonMod_gr_139.gif]
[Graphics:../Images/MilneSimpsonMod_gr_140.gif]

Compute the Milne-Simpson solution based on 200 subintervals and plot the results.
Observe that four fewer subintervals are computed for this case.

[Graphics:../Images/MilneSimpsonMod_gr_141.gif]

[Graphics:../Images/MilneSimpsonMod_gr_142.gif]

[Graphics:../Images/MilneSimpsonMod_gr_143.gif]
[Graphics:../Images/MilneSimpsonMod_gr_144.gif]
[Graphics:../Images/MilneSimpsonMod_gr_145.gif]
[Graphics:../Images/MilneSimpsonMod_gr_146.gif]
[Graphics:../Images/MilneSimpsonMod_gr_147.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004