Testing finite difference approximation

2020 10 12
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更新时间：2020 10 13
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I need to right a script that tests 𝑓(𝑥) = 𝑥^3 at 𝑥 = 3 and determine the second order accuracy numerically by plotting the total relative Error vs Δ𝑥 in a double log plot, where Δ𝑥 = 10^𝑒𝑥𝑝 with the 𝑒𝑥𝑝 varying from 0 to −6 with a step size of 0.25. I have found the second order accurate finite difference approximation for the first derivative of a function 𝑓(𝑥) to be f'(x)=f(xi+Δx)-f(xi-Δx)/2(Δx).
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