Example 5.  Use Richardson's extrapolation and the results of Example 2 and 3 to construct a more accurate solution for 25 subintervals.

Solution 5.

Since the version of the finite difference method we are using is known to be of order  [Graphics:../Images/FiniteDifferenceMod_gr_135.gif], we use the following extrapolation formula.

 

[Graphics:../Images/FiniteDifferenceMod_gr_136.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_137.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_138.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_139.gif]



[Graphics:../Images/FiniteDifferenceMod_gr_140.gif]


[Graphics:../Images/FiniteDifferenceMod_gr_141.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_142.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_143.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_144.gif]
[Graphics:../Images/FiniteDifferenceMod_gr_145.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_146.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_147.gif]
[Graphics:../Images/FiniteDifferenceMod_gr_148.gif]
[Graphics:../Images/FiniteDifferenceMod_gr_149.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004