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Does the following equation make mathematical sense?

$ 2 f(t + dt, x) = f(t, x - dx) + f(t, x + dx) $

Its form appears to resemble a PDE, but I cannot find a way to manipulate the differentials inside the function arguments to demonstrate that idea.

My only thought is to relate $ f(x + dx) $ with the definition of the derivative. That is,

$ \frac{df}{dx} = \lim_{h \to \infty} \frac{f(x + h) - f(x)}{h}. $

However, $h$ is not a differential, and I have run out of ideas. Is my fundamental understanding of a differential variable incorrect, or can the equation above be revived?

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    (Above, I meant heat equation, not wave equation.)2012-06-06

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It could make sense with a change: Subtract $2f(t,x)$ from both sides of the equation, to get $2\big(f(t+dt,x)-f(t,x)\big)=f(t,x-dx)-2f(t,x)+f(t,x+dx). $ If, instead of this, it were $2\frac{f(t+dt,x)-f(t,x)}{dt} = \frac{f(t,x-dx)-2f(t,x)+f(t,x+dx)}{dx^2} $ then you would say it is an approximation to the heat equation $2f_t = f_{xx}$

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    Very clear answer! I think that if I look closely at the steps I followed to obtain the first equation, I might find that there should in fact be a factor of $dt$ and $dx^2$.2012-06-06