Originally Posted by

**davefulton** Hi all,

I'm stuck with how to define $\displaystyle u$

given

$\displaystyle \frac {\partial u}{\partial x}\approx \frac{u_{i+1,j}-u_{i-1,j}}{2\Delta x}$

say I'm incrementing $\displaystyle \Delta x$ and $\displaystyle \Delta y$ at some defined value. I should have a 2D grid with $\displaystyle x_{i}$ and $\displaystyle y_{j}$ down either side and the central values will be $\displaystyle u_{i,j}$.

How do I calculate $\displaystyle u$?

Is it simply $\displaystyle u_{i,j}=\frac{\partial x_{i}}{\partial t_{n}}+\frac{\partial y_{j}}{\partial t_{n}}$

where $\displaystyle t_{n}$ is defined as $\displaystyle n\Delta t$