Two successive first derivative approximations are made using the same finite-di

Question

Two successive first derivative approximations are made using the same finite-difference scheme such that h2=h1/2. The Richardson extrapolation technique ! = 41 (h)-31 (h) is used to improve the derivative estimate. Which of following schemes could have been used in the initial derivative estimate if the result is O(h4)? Note multiple selections are allowed. 4 point centered difference 2 point backward difference 2 point forward difference 3 point forward difference 2 point centered difference 3 point backward difference

Explanation / Answer

The 4 point centered difference should be used in the derivative estimate and is more accurate while using richardson extrapolation technique. Here the truncation error is O(h4) . Also we can use 2 point centered difference as the estimate but will require tiwce the work. But the truncation error will decrease faster.

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