If we want to use the Richardson method to calculate the second order derivative symmetrically at...
If we want to use the Richardson method to calculate the second
order derivative symmetrically at the zero point of a function, how
many points do we need at least?
Give an example of these points we need.
For this case, find the formula for the second derivative.
Homework Answers
Answer
We need atleast 2 points to calculate the Richardson second order derivative.
The small parameter h
denotes the distance between the two points x and x+h. As this
distance tends to zero,
i.e., h → 0, the two points approach each other and we expect the
approximation
to improve. This is indeed the case if the truncation error goes to
zero, which in turn is
the case if f''(ξ) is
well defined in the interval (x, x+h).
For example we have the second order derivative as
To verify the consistency and the order of approximation of above equation we expand
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