What's the difference between numerical method to calculate differential (backward, central, forward)? At what condition do I...

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What's the difference between numerical method tocalculate differential (backward, central, forward)? At whatcondition do I have to use forward over central and backward, etc?If there's boundary condition that permits the complete use ofcentral method, what will happen if I still use forward, backward,and central regardless there's boundary condition that permits theuse of central method?
note: I'm not used to describe pure mathematical problem inenglish, so I'm sorry if my question is hard to understand. feelfree to add comment under this question and I'll explain it again,hopefully in clearer manner. thank you

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Forward difference Consider a linear interpolation between the current data value t0I0 and the future data value t1I1 The slope of the secant line between these two points approximates the derivative by the forward twopoint difference It0 I1I0 t1 t0 Forward differences are useful in solving ordinary differential equations by singlestep predictorcorrector methods such as Euler and RungeKutta methods For instance the forward See Answer

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