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_112.gif], we use the following extrapolation formula.

 

[Graphics:../Images/FiniteDifferenceMod_gr_113.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_114.gif]


[Graphics:../Images/FiniteDifferenceMod_gr_115.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_116.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_117.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_118.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_119.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_120.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_121.gif]

[Graphics:../Images/FiniteDifferenceMod_gr_122.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003