Example 4.  Investigate the behavior of  [Graphics:Images/RichardsonExtrapMod_gr_113.gif].  If the step size is reduced by a factor of  [Graphics:Images/RichardsonExtrapMod_gr_114.gif]  then the error bound is reduced by  [Graphics:Images/RichardsonExtrapMod_gr_115.gif].  This is the  [Graphics:Images/RichardsonExtrapMod_gr_116.gif]  behavior.

Solution 4.

[Graphics:../Images/RichardsonExtrapMod_gr_117.gif]



[Graphics:../Images/RichardsonExtrapMod_gr_118.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_119.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_120.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_121.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_122.gif]

Investigate the  [Graphics:../Images/RichardsonExtrapMod_gr_123.gif]  behavior in the following table of values.

[Graphics:../Images/RichardsonExtrapMod_gr_124.gif]

Step h

  

[Graphics:../Images/RichardsonExtrapMod_gr_125.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_126.gif]

  

[Graphics:../Images/RichardsonExtrapMod_gr_127.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_128.gif]

  

[Graphics:../Images/RichardsonExtrapMod_gr_129.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_130.gif]

  

[Graphics:../Images/RichardsonExtrapMod_gr_131.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_132.gif]

  

[Graphics:../Images/RichardsonExtrapMod_gr_133.gif]

Investigate the  [Graphics:../Images/RichardsonExtrapMod_gr_134.gif]  behavior in the following graphs.

[Graphics:../Images/RichardsonExtrapMod_gr_135.gif]


[Graphics:../Images/RichardsonExtrapMod_gr_136.gif]

[Graphics:../Images/RichardsonExtrapMod_gr_137.gif]
[Graphics:../Images/RichardsonExtrapMod_gr_138.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004