Method | Formula | Error | |||
---|---|---|---|---|---|

Forward difference | $$f'(a)=\frac{f(a+h)-f(a}{h}$$ | $$\frac{-1}{2}h f^{(2)}(\varphi)$$ | |||

Central difference | $$f'(a)= \frac{f(a+h)-f(a -h)}{2h}$$ | $$ \frac {-h^2}{6} f^{(3)}(\varphi)$$ | |||

Four point | $$f'(a)=\frac{-3f(a+4f(a+h)-f(a+2h)}{2h}$$ | $$ | $$ \frac{h^2}{3} f^2(\varphi) | ||

Five point | $$f'(a)=\frac{[f(a -2h)-8f(a-h)+8f(a+h)-f(a + 2h)]}{12h}$$ | $$f''(a)= \frac{f(a) - 2 f(a +h) + f(a +2h}{h^2} $$ | $$ \frac{h^2}{6}f^{iv}(\varphi) - hf''' (\nu) \\ $$ | $$ f''(a)=\frac{f(a-h)-2f(a)+f(a +h)}{h^2} $$ | $$ \frac{-h^2}{12}f^{iv}(\varphi), |\varphi-a|<|a|$$ |

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