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?