- #1
evinda
Gold Member
MHB
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Hello! (Wave)
With what order of accuracy does the divided difference $\frac{f(x+2h)-f(x)}{2h}$ approximate the derivative?
I have tried the following:
$$f(x+2h)=f(x)+ 2h f'(x)+ 2h^2 f''(\xi) , \xi \in (x,x+2h)$$
$$\frac{f(x+2h)-f(x)}{2h}=\frac{2h f'(x)+ 2h^2 f''(\xi)}{2h}=f'(x)+hf''(\xi)$$
$$\left|\frac{f(x+2h)-f(x)}{2h}-f'(x) \right|=h f''(\xi)$$
Thus the order of accuracy is $1$.
Am I right? (Thinking)
With what order of accuracy does the divided difference $\frac{f(x+2h)-f(x)}{2h}$ approximate the derivative?
I have tried the following:
$$f(x+2h)=f(x)+ 2h f'(x)+ 2h^2 f''(\xi) , \xi \in (x,x+2h)$$
$$\frac{f(x+2h)-f(x)}{2h}=\frac{2h f'(x)+ 2h^2 f''(\xi)}{2h}=f'(x)+hf''(\xi)$$
$$\left|\frac{f(x+2h)-f(x)}{2h}-f'(x) \right|=h f''(\xi)$$
Thus the order of accuracy is $1$.
Am I right? (Thinking)