For solving PDE numerically, especially for option which has discontinuity in
initial configuration, it is hard to use high order differention function.
In our test, we find solelly, if we use O(h^2) order approximation to the differention, we can only achieve O(h) order approximation.
If we use O(h^4) order approximation, the error is roughly O(h^2), at this time,
a Richardson extrapolation can reduce the error significantly. (As in this
situation, it is not easy to reduce the space step unboundedly)
Saturday, October 27, 2007
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