Lesson 28
1. What are the different types of difference operators?
2. Why is it that for functions that are 2nd or 3rd order polynomials, the second order central difference operator is the closest numerical difference approximation to the exact second derivative?
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3. Why may it be necessary to extrapolate function values in order to compute difference operators?
4. What is Richardson extrapolation and why is it useful?
The Richardson extrapolation technique enables calculation of the limiting value of a quanitity as the grid size approaches zero, without actually having to reduce the grid size to zero. Thus if it is necessary to estimate the function value at an unknown grid point it is no longer necessary to reduce the grid size in order to reduce the truncation error in the estimate.
5. What is operator calculus?
The difference operators, E, Δ, δ, μ etc. can be operated on using the rules of calculus to find approximation formulas. However this requires making assumptions on the continuity and differentiability of the space of functions on which these operators are defined. Operator calculus can be used to establish relations between the various difference operators.
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