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- Thread starter Silviu
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mfb

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One might be more convenient for the following calculations. It doesn't really matter as you take the limit of ##\Delta x, \Delta t \to 0## later anyway.

In this limit,

$$\frac{\partial P}{\partial x}(x+\frac{1}{2}\Delta x,t)=\frac{\partial P}{\partial x}(x,t) = \frac{\partial P}{\partial x}(x+\Delta x,t)$$

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Chestermiller

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Thank you for your reply! I remember we studied this in a numerical method class. However, why wouldn't one stick to a certain approximation for both space and time?

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Chestermiller

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If you are solving a differential equation numerically like $$\frac{\partial P}{\partial t}=k\frac{\partial^2 P}{\partial x^2}$$you can get added accuracy (for free) in the x direction if you use the 2nd order formula. Sometimes (but not usually) a 2nd order approximation is used for the first derivative in the t direction also; this is called Crank-Nicholson.Thank you for your reply! I remember we studied this in a numerical method class. However, why wouldn't one stick to a certain approximation for both space and time?

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